Once it was discovered about 300 years ago that stars have "proper motion", and appear to move very slowly over the celestial sphere in random difections and random apparent speeds, it was realized that the stars were all moving in three dimensional space.
And if all stars have the same actual velocity in space, or velocities within a relatively narrow range, the stars with the largest proper motion are likely to be nearer to Earth than stars with lower proper motion.
So astronomers naturally tended to try to measure the parallexs of the stars with the largest known proper motions first, since they were probably among the closest stars to Earth. Astronomers also realized that if the different stars all had the same luminosity, the ones which appeared brighter from Earth would have to be closer.
Since the closer a star was to Earth, the larger its parallax would be, and this the easier it would be to measure the star's distance, astronomers concentrated their parallax measuring efforts on the stars which appeared brightest as seen from Earth, and the stars, however dim they looked from Earth, which had the largest proper motion.
The first distance measurements to stars were made in the 1830s, and tens hundreds, and thousands more were made in the next century. By about 1950, attempts had been made to measure almost all of the stars which appear visible to the naked eye from Earth. Many turned out to be too far away for their distances to be measured, and more or less accurate distances to the others were measured. And attempts were made, often successfull, to measure the distances to thousands of stars with large proper motions.
The Hipparocos satellite from 1989 to 1993, and the Gaia space observatory from 2013 toc. 2022, have made many percise astrometric observations of many mthousands andmilions of stars. For example, they have measured the proper motions of millions of stars far more accurately than before. So astronomers might be rushing to measure the parallaxes of all the high propermotion stars they detected.
Except that Hipparcos and Gaia also measured the parallaxes, and thus the distances, of the stars they observed, to much greater accuracy than ever before.
Some astronomers have had projects to discover all the stars closest to Earth and have searched for stars which might be nearby to measure their parallaxes.
Stars with the same spectral class can vary greatly in their luminosities depending on whether they are supergiants, bright giants, giants, sub giants, or main sequence stars. And apparently the spectra of stars can show which luminosity class they belong to.
So astronomers searching for neaby stars would pick luminosity class V stars, main sequence stars, to find the parallaxes of, because they would be much less luminous that giant stars with the same apparent brightness, and so would be much nearer.
So discoveries of stars that are really close to the Solar system has slowed down a lot as the lists become more and more complete.
The 1991 third Gleise catalog of stars within 25 parsecs (84.64 light years) of the Sun includes 3,803 stars. A sphere with a radius of 25 parsecs has a volume of 65,449.8469 cubic parsecs. So the stars in the catalog have a density of about 0.0581055 stars per cupic parsec.
Wikipedia's List of nearest stars and brown dwarfs lists stars and brown dwarfs within 5 parsecs of the Sun. That list has a volume of 523.598776 cubic parsecs. Omitting 11 brown dwarfs, and including the Sun, there are 65 stars in that radius. So the stars in that list have a density of 0.1241408 stars per cubic parsec.
However, the individual stars in the list are grouped in star sysems containing 1, 2, or 3 stars each. There are 50 star systems in the list, so the star systems have a density of 0.0954946 stars per cubic parsec.
I am not certain whether the Gleise catalog lists individual stars or star systems. So I don't know if the stellar density of listed stars in the Gleise catalog is 0.4680612 or 0.6084689 the density of stars in the list of nearby stars.
Either way, it indicates that the percentage of stars whose distances have been measured decreees with distances of just tens of parsecs.
There is another class of astronomical objects sort of similar to stars. Tthey are called brown dwarfs, intermediate in mass between planets and stars. Since brown dwarfs have only limited fusion during parts of their lifetimes, they are very cool, compared to the typcial star, and emitt almost all their radiation in the infrared bands.
In recent decades many brown dwarfs have been discovered. The closest examples are Luhman 16A & Luhman 16B, and WISE 0855-0744, (both discovered in 2013), at distances farther from the Sun than Barnard's Star, the second closest star system, and closer to the Sun than Wolf 359, the third closest star system. There are a total of 11 brown dwarfs within 5 parsecs.
So probably some more brown dwarfs close to the Sun will be discovered.