I will always remember when I first got into serious proof-based math in the first semester of college, and I had to work hard to develop my sense of what counts as a sufficient proof. I would read the proofs in the textbook and hit the QED at the end and not understand why it was enough. Eventually I came to understand something like the framing here, which is that a proof is about persuasion, persuasion is about judgment, and judgment (by definition, maybe) can't be pinned down to clear rules.

The University of Chicago has a special math class format called Inquiry-Based Learning designed around this idea, where you work together in class to put proofs together and work out a shared understanding of what is sufficient. I didn't take it but I wish I had. You can read some people's experiences with it here[0].

[0]: https://www.reddit.com/r/uchicago/comments/i1id9e/what_was_y...