I had the same issue, but none of the suggested workarounds worked for me. However, I think I may have figured out what was going wrong.
By default, Unreal Engine saves new projects in the Documents folder. I had my Documents folder syncing to OneDrive. When I opened the project folder, I noticed some files had an icon indicating that a sync was still pending (even when the project is closed). They were TMP files, and even after waiting for a while, they never got synced. I wonder if Microsoft intentionally ignores syncing files with a certain extension, seems like that would make sense… but in any case, because they were marked as “sync pending”, they were essentially locked. When I tried to move the project folder outside of OneDrive (using Windows Explorer), it wouldn’t let me for the same reason.
I just ended up copying the entire Unreal Projects folder, moving it outside of Documents (and therefore outside of OneDrive). I was able to open the project it just fine afterward.