I have just experienced this serious issue. I left the GIS server running an analysis overnight. When I got back to it this morning, the analysis had completed. I attempted to close ArcGIS Pro, but the project failed to save (I didn't record the error at that point). I then closed it without saving, as nothing in the project itself should have changed recently (just the data).
Then I attempted to re-open the project, but it didn't exist (same errors as others have found here, including missing .aprx file)!
There were no backups in the projects ".backups" folder, so I've now had to log a job with our IT people to have the .aprx file recovered from their backups.
This is a fairly horrific experience, being fairly new to ArcGIS Pro, and about to start transitioning our entire organisation to Pro.