Is there any absolute evidence of star formation inside of nebulae (AKA stellar nurseries) as is suggested and even stated as fact by many textbooks?
In science there is no such thing as an irrefutable fact, there is just the best theory we currently have that explains all the data and makes sense. That is very different from an assumption.
A theory is something that you can test - make models and predictions and check that they match up to real life. An assumption is something that you don't have evidence for but you think it should make sense, so you choose to believe it.
Our current understanding of star formation and stellar nurseries is an excellent theory - it has been around for a long time, built up of many parts that have each been tested and confirmed, it matches observations in many ways. It's not perfect and there are still things we don't know (otherwise scientists would have no jobs) but in high school level textbooks we can reasonably present this as a 'fact' because we are pretty certain it won't change any time in the next 50 years.
An assumption would be like me assuming you are reading a high school textbook. It fits the facts (the level of detail in your question) but I haven't tested it (asked you about the book).
Nothing in science is "irrefutable", but some things are well enough established that only a fool bets against them. Theories of stellar birth in nebulae are close to being in that category. (But the devil can still be found lurking in the details.)
One of the things that give us confidence that a theory correctly describes the world is when it is large, covering a wide range of phenomena with only a small set of moving parts. The idea that the galaxy started as hot gas which condensed into stars and planets explains a very great many facts without any special assumptions (meaning without assuming anything we can't verify in the lab) except the assumption that there was a large cloud of relatively cool gas and dust to begin with.
Given that, we can see how the laws of physics discovered in the lab cause the cloud to break into smaller, denser clouds each of which then collapses in multiple places forming a cluster of new stars of the same age embedded in the remains of the nebula. And those same laws of physics show that some of the gas and dust that doesn't make it into the new star will condense into planets.
It's a very parsimonious explanation. I know of no alternative explanations for stars which don't assume a bunch of new stuff we haven't seen in the lab or, worse, assume stuff which contradicts what we've seen in the lab.
On top of all the physics, astronomy observes clouds of gas and dust and clusters of stars and all the things in between. The process is too slow for us to have watched a specific star start as a nebula, condense out, and end up shining in empty space, but we see all the stages. (It's like seeing a crowd of people from little babies to young adults to the elderly -- even though you don't have time to watch a baby grow up, it's much more reasonable to conclude that you're seeing individuals of the same species at different stages of their life cycle than that you're seeing many different species.)
The theory is also strong because it is easily falsifiable. Strong theories make predictions which can be tested and which might fail the test. Weak theories are so vague or hand-waving that they can accommodate any observation without failing.
So that stars condense out of clouds of gas and dust is rock-solid science. As with any science, we need to always be prepared to change our theories when confronted with new observations...but not before.
(There is still a lot we don't know about the details of the whole process that turns a cloud of gas and dust into a planetary system -- it's a hot topic of current research. But so far, anyway, there's nothing visible that suggests the basic theory is wrong; just that the details are complicated enough to keep us working to understand them.)
Good question but what would you call absolute evidence? There is evidence that these nebula regions contain a large number of very young stars. A larger number than one would expect to find in a normal or regular region of space. I don't know if you consider that absolute evidence but absolute evidence may require us to view things that cannot be seen from afar. So we have to make assumptions. Hope this helps.