If you currently have the data on Firefox on a computer, there's not really any need to back anything up. Resetting your password doesn't delete any data that's already synced to your devices, just the copy of the data on the Firefox Sync server.

If you want to make a copy of your local data, you need to make a copy of your profile folder. See Back up and restore information in Firefox profiles.

Hope this helps.

See also:

• https://support.mozilla.org/en-US/kb/reset-your-firefox-account-password-recovery-keys

When I go to reset my password it says "NOTE: When you reset your password, you reset your account. You may lose some of your personal information (including history, bookmarks, and passwords). That’s because we encrypt your data with your password to protect your privacy. "

The message is referring to the data that is stored on Firefox Sync, not the data that has already been transferred to your device(s).