If I build their slicer, not modifying any line of code, then accessed using that binary, would that be acceptable? If not, why not, considering it is identical to what is on their website?

If I made any changes prior to building, would it still be acceptable? And if not, where is the line? What is the legal basis, any precedent? How much of the code may I modify before I cross an invisible threshold and somehow "bypass" an "authentication" (neither fit UA anyways, either for law or other purposes unless one can provide any evidence that it ever has).

Even if that’s correct, Bambu has a right to then press charges on the users, but can’t really complain about the guy simply copying AGPL software to make it work. He’s not the one doing the illegal part.

Bambu clearly didn’t want to press charges on their users, though, so they weaponized the law to try and prevent this, and it’s causing them issues.

In any case, we’re not in some “only the laws matter” reality, we’re also have ethics and morals to consider, in which case Bambu is clearly in the wrong. If they want to secure their servers, they should do it properly rather than using legal threats.