I am an infrequent user, mainly for basic cartography purposes. This issue had me pulling my hair out, especially because I'm certainly not as well-versed or as fast as the pros, and rebuilding entire sets of maps and layouts that took me days to make were simply not an option. I lost access to a .aprx file back in April, and have been living without access to quite a bit of work saved in that file.
After being tasked with a project that would involve rebuilding much of what was in the file, I spent some time trying to recover it. Happy to report I did so successfully. One important thing to note: My file, which was displaying the exact same reported error as the OP, did in fact still have a file size (632kb), unlike several others with this issue that had reported their file size at 0 after experiencing this error.
Here's what I did:
1. Copy the project file (not the entire folder) to a place on your local machine (e.g. desktop)
2. Rename the file by replacing the ".aprx" file extension with ".zip"
3. Try opening the file with file compression/extraction software such as WinZIP. In my case, I was unable to open the file. If in your case, you're able to open the file here, you probably have a different issue than I did.
4. Run the .zip file through a repair program. WinZIP has one built in. After the file is repaired, you should be able to see the contents as a list of folders and files, including "map", "layout", "007Index.ind", "documentInfo.xml", as well as several hex-coded .xml files.
5.***Make a back-up copy of your entire project folder before proceeding***
6. Rename the .zip file back to the original project name with the .aprx file extension
7. Overwrite the "broken" .aprx file with the repaired one
8. Cross your fingers and open the project file from windows explorer. In my case, I got a dialog stating "The project file was corrupt but has been repaired. You must restore references to external items such as folders, databases, and toolboxes manually." I restored connections to the geodatabases I had been originally using in the project and all maps and layouts appear to be intact.