Thanks for your posting. A database restore would revert the entire database and affects all projects, that's correct. Another solution would be to restore a database backup to a second database, set up a staging installation and then export the test suites & cases using TestRail's XML export (and then import the cases again).
You can set up a stating/temporary installation as follows:
If you have a recent closed test run in the production instance, you can also export this test run and we can convert this into a valid export for the test suites/cases again. If this would be an option, you can send the XML export of the closed run to our help desk at firstname.lastname@example.org.
I hope this helps!