FCPX Project disappeared suddenly

This is while the application is open or closed?

The library structure looks quite unusual. The event is called All Vids? What's inside there? That's where Original Media and Transcoded should be as well as the projects 1st game and Untitled. What are you seeing in the library? Can you send a screenshot of the library browser?

The folder Untitled Library is designated as the storage for backups? Untitled is your only library?

What happens when you trash preferences? Does the application create a new Untitled library in the Movies folder.

Just to be completely clear: you have the library open and then choose File->Open Library->From Backup...

choose a date where you are sure you were editing this project, and it is not there? Super weird...

Is it possible that you have edited inside a clip instead of a project? Sorry if this is obvious but it’s a mistake that we see often.

See if there is a clip with a duration that could match the duration of your edit.

Under the library in the browser sidebar there are Smart Collections. Among them is one called Projects that should show you just the projects that exist in the library. Is that empty?

That isn’t where a project should be. Can you post a screenshot of this

project in the __snapshots file in currentversion.fcpevent format when I entered the package content of the library

in column view to see the library structure.

That's extremely weird. Can you post an Etrecheck report? Give it Full Disk Access and copy and paste into your reply using the "Additional text" button below.

This is very odd. When you say you looked through backups, do you mean FCP's automatic backups in your ~/Movies/Final Cut Backups/ folder? Or your TimeMachine backups?