Is Buzz Lightyear forgetting his origins like Woody?
According to the answers here Why is Buzz the only toy that does not believe he is a toy? a toy starts its existence thinking it is the character it is based on, then it realizes its true nature as a toy and accepts it. We don't know the rest of the process.
In the case of Buzz, I saw this:
Toy Story: he is a new toy, he thinks he is the character he is based on. Then he realizes he is a toy and accepts it.
Toy Story 2 and Toy Story 3: Buzz keeps the skills and the determination of a hero character, he remembers his backstory. I suppose the Buzz Lightyear cartoon is long cancelled in Toy Story 3.
Toy Story 4: Buzz is all doubtful about what to do next, he doesn't behave like an action hero anymore. He even has to ask his recorded quotes for advice.
I can conclude that, given enough time, a toy forgets its origins completely. This didn't happen to Gabby, the Prospector or Jessie because they were exposed to their merchandise or the info in their original boxes.
So, in Toy Story 4, is Buzz Lightyear going through the last phase of a toy's existence when he forgets his origins, like Woody?
I don't think Buzz has forgotten who he thought he was (i.e. his toy backstory). Quite the opposite, he remembers it and it makes his real life look comparatively bleak (more so than for the other toys), which is weighing on him and significantly impacting his character as time goes on.
Buzz's issue is that he is a toy with a highly promising backstory. In comparison, real life is bleak. He's not a hero, he's not saving the innocent. He's just a "man" (character wise).
Comparatively, the other toys we tend to meet don't have such high personal expectations of themselves as a toy. They're a dinosaur, or a potato, or a slinky dog. There's no real backstory to them. The one exception I can think of are the toy soldiers, but they seem to be quite simple of character, not capable of complex emotions (as far as the movies explore, at least) and continue their soldier-like attitude regardless.
Woody, while having somewhat of a backstory, is sort of still leading the same life that he would in his backstory. He's the "sheriff" in his group town.
Buzz is a complex character, and his toy background has set him up for tremendous disillusionment in real life. He doesn't live up to his own idea of himself, and he started from a really high spot, so his fall has been bigger.