I am not familiar with webdav, and I’m no bazzite expert (although it’s my daily driver), but I would guess that distrobox could be a way to do this.

Either install a distrobox of arch or mint or Debian or whatever, and do the install there, or check out what distrobox has to offer for mounting WebDAV storage. I found it has options for implementing local AI that I would never have dreamed of, so who knows what else it can do?

https://docs.bazzite.gg/Installing_and_Managing_Software/Distrobox/

That’s supposed to be the last resort though, when nothing else works.