The only way would be using an older copy of key4.db that doesn't have a PP or a known PP.

• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

You can look a utility to browse System Restore points.

• https://www.shadowexplorer.com/
• https://www.nirsoft.net/utils/shadow_copy_view.html

Do you still remember the old Primary Password? And do you have a backup of your profile folder made when you were still using the old Primary Password?

Would changing the Primary Password prevent the passwords stored in "logins-backup.json" from unlocking with the old Primary Password?

I am not sure how it works, but if each of the files "logins.json" and "logins-backup.json" are encrypted with the Primary Password that was in effect when they were written, then recovery would be as simple as replacing the former file with the latter backup?

That said, the first thing I would do before attempting any recovery or doing anything else, wuld be to backup the files "logins.json", "logins-backup.json" and "key4.db", in the profile folder.

The logins.json file is always encrypted with the same encryption key using a specific seed generated when key4.db is first created. When you do not use the PP then this encryption key is stored directly in key4.db. If you use the PP then this key is encrypted with the Primary Password, but logins.json remains unchanged.