Time Machine (left running) will backup everything, if you move a file you would have to find it at the old location. It will backup incrementally until you run out of backup space, then it deletes the oldest stuff first.
But if you’re not running it no point looking for it.
You really need to adopt some sort of backup strategy, so in the future, you can recover easily. Time machine works very well and is included with MacOS, all you need is an external drive (pretty cheap nowadays).
It sounds like the project file may be corrupt. If that’s the only copy that means you may have to rebuild it from the existing site. Now if it was a RapidWeaver 7 (or greater) project, there was an option to “backup” the project file to the server when you publish. If you had that option turned on in the publishing settings it might have been backed up for you.
If you think you may have turned that option on then check on the server (host company) for a folder(directory) that will have a strange looking name like