When you see this error on the screen, press F12 and check for error messages in the Console tab. There's usually an explanation why the project can not be opened - for example a missing file etc.
Then you can rename the project to .ZIP, extract it to an empty folder and try to fix the issue.
Before doing anything, make a couple of backup copies of the project first!
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Also, maybe you do have automatic backups - check "Save & Backup" section in Construct 3 Settings.