working on files on a WebDAV mount on Big Sur 11.4 with M1 chip

The only thing you are missing is assuming this problem has something to do with Big Sur or the M1 chip. Apple's WebDAV implementation has not worked reliably for years. In fact, from your description of the problem, it sounds like Big Sur has made significant improvements in WebDAV functionality.

I'm afraid your only option is to use some 3rd party app like Transmit.

For reference, back in Mountain Lion days, I wrote a little app that used WebDAV as an intermediary to allow users to connect to remove FTP and ssh file servers and mount them on the desktop. Normally, this requires some system modification like FUSE. I did it in the Mac App Store. Since my app actually lived on the other side of WebDAV, acting as a server, I was able to see the internals of how Apple implemented WebDAV. It was downright horrifying. In Mavericks, Apple introduced a bug that would reliably break my app completely. Since users were sure to blame my app instead of Apple, I had no choice but to discontinue it. When I inquired directly with Apple, they were not surprised and said they had no plans to correct any WebDAV bugs. They suggested I use SMB instead. However, SMB is significantly more complicated to implement so I didn't bother.

A few years after that, I had an opportunity to work at an organization that had top-of-the-line SMB servers and a very fast network. Even in that environment, Mac networking was hit-or-miss. From your list above, I was able to do 1. and 3. reliably. I was also able to solve 4. using autofs. Unfortunately, Apple no longer supports autofs. It still seems to work, but Apple purged the internet of its excellent autofs documentation. That makes it difficult to recommend autofs to people here on Apple Support Communities when the only available documentation is some bootleg copyright violation that I can't link to in the Apple forums.