restoring projects stored locally

[Art Ko]

Hi,
I'm new to Pro Tools First and most likely did something stupid, not understanding how the program creates backups and cache. Tried to find an answer in knowledge base or elsewhere in google - no luck. I really hope someone can help me out.
I had two projects stored on the cloud, the rest were stored locally. Yesterday the two projects stored on the cloud opened empty. There was a comment "not available" near them. The files stored locally opened fine. I backed up the "Project Cache" folder, reinstalled Pro Tools First. The projects stored on the cloud still would not open. Then I placed the locally backed up "*.ptproject" folders of the two projects that were online, in the new, now empty "Project Cache" folder - and the projects opened. I was very happy - but when I put into this newly created "Project Cache" folder other locally backed up "*.ptproject" folders - Pro Tools First just doesn't see them((
Those locally backed up "*.ptproject" folders opened yesterday, and I see all the files inside, including the .wav files in "Audio" subfolder... Is there any way to save those projects stored locally from the backed up files ("Project Cache" folder) now?
I would appreciate any thoughts. Thank you.