By asking if a planet can be bigger than its star, are you asking if a planet can be more massive than its star or can a planet have a larger radius and volume than its star?
Part One: The relative masses of stars, brown dwarfs, and planets.
The Sun, a fairly typical star, has a mass about 300,000 times the mass of the Earth, a fairly typical planet. So any fairly typical star will be many thousands of times as massive as any fairly typical planet.
The planet Jupiter has 317.8 times the mass of the Earth, or 0.000963 the mass of the Sun.
The dividing line in mass between the most massive planets and the least massive brown dwarfs (which are considered a third class of objects) is about 13 Jupiter masses or about 4,131.4 Earth masses, or about 0.0125193 the mass of the Sun.
The dividing line between the most massive brown dwarfs and the least massive luminous stars is about 75 Jupiter masses, or about 23,835 Earth masses, or about 0.0722272 the mass of the Sun.
So as long as brown dwarfs are considered to be separate types of objects from either planets or stars, the least massive stars must be about 5.76 times as massive as the most massive planets.
But if brown dwarfs are considered to be either very massive planets or very low mass stars, then the mass range of planets and the mass range of brown dwarfs would meet. And it is possible that extreme changes in the chemical composition of objects would determine which class they fall into despite their mass.
So if brown dwarfs are considered to be either planets or stars, there could be a small overlap in the mass ranges of planets and stars due to their chemical composition. And there could be rare examples of planets slightly more massive than stars, or stars slightly less massive than planets. And in very, very rare cases, a system could consist of a super rare star less massive than the most massive planets and a super rare planet more massive than the least massive stars, and so have a planet slightly more massive than its star.
In those cases the planet and the star would have almost identical orbits around their center of mass, but the orbit of the planet would be a little smaller than the orbit of the star, so some people might say that the star was sort of, of kind of, in a way, orbiting the planet.
But this depends on brown dwarfs being classified as planets or stars instead of as a third class of objects So long as brown dwarfs are classified as a third class of objects most stars will have thousands or millions of times the mass of most planets, and even the least massive stars will be over five times as massive as even the most massive planets.
Part Two: Size - radius, diameter, and volume.
There is an interesting fact about the sizes of high mass planets, brown dwarfs, and low mass main sequence stars. They are all about the same size. Increases in mass beyond a certain limit cause increases in density instead of increases in size.
So - with rare exceptions - planets do not get much larger than Jupiter no matter how massive they get. Jupiter has a mean radius of 69,911 kilometers or 43,441 miles.
Planets with the mass of Jupiter and above, brown dwarfs, and low-mass red dwarf main sequence stars all have about the radius, diameter, and volume of Jupiter.
And there are a few known examples of red dwarf main sequence stars with smaller radii than the planet Jupiter, and thus smaller than planets which are slightly larger than Jupiter.
The second smallest star known, 2MASS J0523-1403, has a radius of about 60,000 kilometers or 37,000 miles, 0.86 the radius of Jupiter and 0.086 the radius of the Sun.
The smallest star known, EBLM J0555-57, has a radius of about 59,000 kilometers or 37,000 miles, 0.84 the radius of Jupiter and 0.084 the radius of the Sun. It is slightly larger than the planet Saturn though hundreds of times as massive as Saturn.
So there should be rare solar systems where a very small red dwarf star smaller in size than Jupiter is orbited by one or more very large planets as large as or even larger than Jupiter (along with possible smaller planets). Thus there should be rare star systems which have planets slightly larger than their stars, though much less massive than their stars.
There is an exception to planets not getting much larger than Jupiter. In our solar system the giant planets with their extensive atmospheres of hydrogen and helium all orbit far from the Sun and are cold.
But the larger and/or more massive an extrasolar planet is the easier it is to detect. And the closer an extrasolar planet is to its star, the easier it is to detect. So most of the earlier planets discovered in other star systems were very large and/or very close to their stars, and it was learned that giant gaseous planets can sometimes orbit very close to their stars.
So some giant planets in other star systems orbit their stars close enough to be as warm as Mars, some orbit close enough to be as warm as Earth, some orbit close enough to be as hot as Venus, and some orbit close enough to be much hotter than any planet in our solar system.
The hottest known exoplanet, KELT-9b, has a temperature of about 4050 ± 180 Kelvin. 4050 K is about 6830°F.
And when gas giant planets get very hot, their atmospheric gases expand, and their atmospheres get very large. Such very large and low density hot planets are called "puffy planets" or "hot Saturns".
Gas giants with a large radius and very low density are sometimes called "puffy planets" or "hot Saturns", due to their density being similar to Saturn's. Puffy planets orbit close to their stars so that the intense heat from the star combined with internal heating within the planet will help inflate the atmosphere. Six large-radius low-density planets have been detected by the transit method. In order of discovery they are: HAT-P-1b, COROT-1b, TrES-4, WASP-12b, WASP-17b, and Kepler-7b. Some hot Jupiters detected by the radial-velocity method may be puffy planets. Most of these planets are around or below Jupiter mass as more massive planets have stronger gravity keeping them at roughly Jupiter's size. Indeed, hot Jupiters with masses below Jupiter, and temperatures above 1800 Kelvin, are so inflated and puffed out that they are all on unstable evolutionary paths which eventually lead to Roche-Lobe overflow and the evaporation and loss of the planet's atmosphere.
The exoplanet with the largest radius may be TYC 8998-760-1 b with three times the radius of Jupiter or about 209,733 kilometers.
However, TYC 8998-760-1 b has mass of 14±3 times the mass of Jupiter, between 11 and 17 times the mass of Jupiter. Since the dividing line between planets and brown dwarfs is about 13 times the mass of Jupiter, there is a good probability that TYC 8998-760-1 b could be a brown dwarf instead of a planet.
And apparently its radius is not measured very accurately. Wikipedia says the planet with the largest accurately measured radius is HAT-P-67 b with twice the Radius of Jupiter or about 139,822 kilometers.
HAT-P-67b has the largest accurately measured radius, at 2.085+0.096
This list also makes HAT-P 67 b the largest object that is probably an exoplanet.
So it is safe to assume that the largest puffy planets can have at least 2 times the radius and diameter of Jupiter. And it is possible that some puffy planets are much larger than that.
So it is possible to have a star system where a puffy planet with at least two times the radius of Jupiter orbits a red dwarf star with only about 0.85 the radius of Jupiter. Thus the planet can have 2.35 times the radius and diameter of its star.
But the planet can only be hot enough to have such a vastly inflated atmosphere if it orbits very close to its dim red dwarf star. The orbital period should be days or hours long instead of months or years for the planet to be super hot.
There are other types of stars beside main sequence stars. After stars complete their main sequence periods they swell up into red giants, and go through other phases before becoming white dwarf stars.
The more massive a white dwarf star is, the smaller and denser it will be. No white dwarf can be heavier than the limiting mass of about 1.4 the mass of the Sun.
GRW +70 8247 is listed as the smallest white dwarf with a radius of 3,300 kilometers or 2,100 miles, 0.52 the radius of Earth, 0.047 the radius of Jupiter, and 0.0047 the radius of the Sun.
So some white dwarfs can be so small that almost all planets will have larger dimensions.
However, this lists includes two smaller white dwarfs.
ZTF J1901+1458 (nicknamed Z; formally ZTF J190132.9+145808.7; Gaia ID 45068691282796485121) is a white dwarf, about 135 light years away roughly in the direction of Epsilon Aquilae, discovered by the Zwicky Transient Facility circa 2021. It is the most massive white dwarf yet found, having 1.35 times the mass of the Sun, nearly the largest expected mass for this type of object. Its radius is about 2,100 km (1,300 mi),2 about the size of Earth's Moon, and it rotates once every 7 minutes.3
A normal gas giant planet with a radius of 69,911 kilometers or maybe as much as 100,000 kilometers orbiting a white dwarf star with a radius of only about 2,000 kilometers would probably be an extreme enough example of a planet being larger than its star to satisfy anyone.
A super hot puffy planet could have an ever larger radius of 139,822 kilometers or even more, but a planet super close to its star would have been swallowed up when the star expanded to be a red giant. Thus a surviving planet of a white dwarf close enough to be a puffy planet would have had to have been far from the star when it was a red giant, and become a close puffy planet it would have had to have gradually spiraled inwards after the star was in the red dwarf stage.
A neutron star is the remnant of a more massive star which became a supernova and blew away most of its mass.
The smallest neutron star is listed as PSR B0943+10, with a radius of 2.6 kilometers or 1.61 miles, a tiny fraction of the radius of Earth, let alone that of Jupiter or of the Sun. Though it has been suggested that it is actually an even more exotic quark star. Of course a supernova should destroy the planets orbiting them, so neutron stars should not have planets.
But the first confirmed discovery of an extrasolar planet was in 1992, of a planet orbiting the neutron star PSR B1257+12. PSR B1257+12 is now known to have three planets, which are named Draugr, Poltergeist, and Phobetor. Draugr, or PSR B1257+12 A, is the smallest known exoplanet, with about 0.020±0.002 the mass of Earth - Earth's moon has a mass of 0.0123 Earth's mass.
In 1992, Wolszczan and Frail discovered that the pulsar had two planets. These were the first discovery of extrasolar planets to be confirmed; as pulsar planets, they surprised many astronomers who expected to find planets only around main-sequence stars...
The planets are believed to be the result of a second round of planetary system formation as a result of two white dwarfs merging with each other into a pulsar and a resulting disk of material in orbit around the star. Other scenarios include unusual supernova remnants or a quark-nova. However, the white dwarf–white dwarf merge model seems to be the most likely cause of the formation of the planets.
So even tiny Draugr should have a radius of nearly 2,000 kilometers, unless it is made of some very dense form of matter, And the other two planets are more massive than Earth. Thus they should all be many times as large as PSR B1257+12 which is estimated to have a radius of 10 kilometers.
And PSR B0943+10,the smallest known neutron star, happens to be orbited by two gas giant planets over twice as massive as Jupiter, which must seem huge compared to their star.
Of course a more massive star than one which ends up as neutron star ends up as a stellar mass back hole. But there are no known exoplanets orbiting around black holes.