It's kind of a philosophical question at this point about what actually comprises a valid proof, if other mathematicians can't make use of it.
So the conjecture is still mostly considered unproven. That could change at any point but there have been no real advances in some time.
[1] Section 1.12 of https://www.kurims.kyoto-u.ac.jp/~motizuki/Essential%20Logic....
This is an understatement. He developed a completely different branch of mathematics through papers that spanned hundreds of pages with very dense and very different ideas from mainstream mathematics.
If it was just slightly obscure, maybe all but half a dozen mathematicians in the world might be able to understand his work. As it stands, at it's best, his proof is so opaque that even the brightest (Scholze) can only kind of understand it. At it's worst, they've rightfully identified it as flawed and that even Mochizuki himself doesn't understand that it's wrong.
The assumption at this point is that it's broken.
The onus is on Mochizuki to either clarify the proof or use the tools of the proof on some other already established problem to show their validity.