We are all fellow users here, save for the occasional Apple community specialist assigned to the Apple community host team.
I have macOS 11.4 (20F21) on an M1 mini, and I have absolutely no issues with multiple Preview sessions on the same or different PDF losing prior annotations (my term for edits). My PDFs are opened and saved to the local boot drive, not Apple's or another cloud service, or not to a Windows server share. I do not run any anti-virus product, or use any so-called cleaner applications that may harm application internals. Not insinuating that you do, but stating what I don't do…
You may have some twisted cache, or Preview configuration data causing your issues. If it was a bug, I would have it too.
What you can try, with no promise it will fix Preview, are the following:
- Boot into Safe Boot mode, and then reboot normally, and then see if the Preview issues persist. Safe Boot is doing several housekeeping chores and will take much longer in the boot cycle. There may be some harmless screen artifacts too.
- In your /Users/username/Library folder, after quitting Preview
- Look in the Caches folder for anything related to Preview and move it to the Trash.
- In the Application Support folder, locate the Preview folder and drag it to the Trash.
- In the Preferences folder, move com.apple.Preview.LSSharedFileList.plist and com.apple.Preview.plist to the Trash.
Once the above is done, launch Preview again, and test if the previous behavioral issues are gone.