Yes, there was a .sync folder, and the version.txt file just had the number "2" in it.
Hmm, that's strange that it's trying to update that file if it already contains 2 in it. The errors seem to point to some kind of access issue, but I'm not sure what particularly is causing the error.
To be honest Joplin sync with NextCloud servers over WebDAV has a lot of reports on the forum of running into strange issues like this, usually after some kind of upgrade or network configuration change, which the user may not know about (if hosted) or didn't expect to be relevant (if self hosted).
Are you able to admin the full NextCloud instance? May not be relevant to your error, but one thing that springs to mind is that a recent new version of NextCloud broke Joplin sync due to simply having certain NextCloud apps pre-installed. I think it was either a Maps or Gallery app, but if you're able to disable the other apps yourself, try disabling all apps except whatever provides the WebDAV service, and see of that helps.
Yeah, everything about this is strange, and I'm tipping on some unknown, cryptic detail somewhere in access as well. I hadn't seen that there were other reports of weird stuff with NC on the forum, so that's good to know. Maybe it's just time to try Joplincloud. I like the self-hosted option, but not if I have to become an expert to use it (I have other things I'd like to do, in life 
). I'll see whether other things were installed automagically - I don't remember it, but I am theoretically the Admin. Thanks again! 
I was just looking around again and found 1 more thing and thought it might mean something to you. The readme.txt next to the version.txt file said that version is now kept in info.json, and looking in that file, the version appears to be "3", not "2" like in the txt file. There also was an error originally somewhere that mentioned not being able to do something with info.json. Does this help? Thanks again!
That just makes it even more weird that it wants to update the version.txt file, when info.json has the version set to 3