Disclaimer: "Don't do this at home" I'm not from Autodesk and I have no idea what I'm doing. I'm just an end user that was disappointed there wasn't a fix for this error.
This error was really annoying me and I was about to start un-installing and re-installing in an attempt to fix the issue .
Before I did this I found a support article that suggested running
Fusion.CancelUploads/force
in the File->View->Show text commands window
as a possible solution to the problem.
Unfortunately this didn't fix the problem for me but it did mention something about the following folder
C:\Users\username\AppData\Local\Autodesk\Autodesk Fusion 360\YWB5MQ6EN5R3
So I thought YOLO, what have I got to lose, I'm about to reinstall everything anyway. I'll delete this folder and see if this either does nothing, breaks everything and I have to re-install, or maybe it might delete the file that is causing the issue.
NB: Before I deleted this folder I went searching through this directory and found one fusion file will some weird name, deep down in some folders. I opened this file (Again, probably something you shouldn't do from inside appdata) and I noticed that it was a project I was working on around the time that this problem all started. So I thought I'd delete the folder and see what happens.
Anyway, when I restarted fusion this folder and all it's subfolders was recreated and the problem was fixed, no more error message every time I closed fusion.
I know messing with the appdata folders is something that shouldn't be done and I'll probably regret it latter on when some other part of fusion 360 breaks because I did this. But at the moment everything is working and I've delayed having to un-install and re-install everything. What I'm really hoping is, that someone from Fusion 360 support will read this post and see that end users are getting really frustrated with this error and are willing to try anything to fix the problem so they might offer some "correct" method to fix the issue.
My advice, don't do this fix unless you are prepared that it might break everything and you will have to re-install.