Update: something I did yesterday must have helped because today I was able to save files I couldn't since last wednesday, with the exception of the first file where I noticed this issue, which still has the "Releasing Reservation" status as shown in my previous message.
I generated a share link to the file that first had this issue, in case people want to check it out: https://a360.co/40OB96r
When I sent it to support last week they said no issues were found with this file in the machine, so I assume it is either my account or my machine, which is why I did all the repairing/reinstalling yesterday.
I tried to upload the 142mb .f3z downloaded from that link and after almost an entire hour it had only succeeded in uploading 4 of the 120 files in it (and those 4 were up seconds after the upload began). For reference, friday I did the same thing and it uploaded 2 of those 120 in about the same time.
I then logged into another account in the same machine, tried to upload the same .f3z with it and it worked with no issues, so I guess the problem is related to my account somehow.
The only thing I can think of right now that might help is to delete the folder of this account in the AppData/Local/Autodesk/Autodesk Fusion 360 in case it's some local cache issue that wasn't deleted in yesterday's steps. I might try that later today, I'll just wait a bit in case I hear something else from support.