A theory is something that has strong supporting evidence, and if you agree with Popper and Kuhn and various" Historians or Philosophers of Science", something that skilled people have tried to come up with alternatives, tested them, and the theory has survived where they didn't. Ideas that have been proposed, and maybe have a little supporting evidence, but are considered not tested enough, and not studied rigorously to see if they can be falsified, or if some other idea better fits Occam's razor, are called hypothesi (or often just interesting ideas until they get at least a little support). Yes, just who qualifies as skilled, which idea is actually simpler by the razor, how much testing is enough, and 'how much better at predicting what than the competing ideas are' are all somewhat subjective, and individual scientists are not exceptionally flawless at making those judgement calls. But that's true of just about everything. Science works because the method tends to correct for those subjective aspects, not make them more powerful as in so many other areas of human activity.
By this era, the theory that the sun was powered by Fusion of Hydrogen into Helium had a lot of evidence supporting it, such as the abundance of various elements in it and other stars, as determined spectrally. Try a web search for Hans Bethe if you want to know about the first evidence that helped raise this hypothesis to the status of theory, in 1930, although he didn't get the Nobel for his work until 1967. It's interesting to me that people are debating just what counts as a theory, and for this particular case, there's an exact date when a particular paper was published, and widespread agreement that this date and event is when the hypothesis got enough support to start calling it a theory. This is additional evidence that adds more support, and by the Philosophers of Science, ought to mean anyone who thinks they have a better idea will have to gather even more evidence and work even harder if they want their alternative to be taken seriously.