Is there a way to see a history of passwords created by the 'generate ...

Firefox offers to update the password before the password change is complete. It would be more stable if old passwords were retained until we delete them.

Firefox keeps your passwords in your profile, and in most/all versions since v2.0 this data is encrypted.

Firefox's password management feature securely stores your usernames and passwords. Learn how to save, view, manage and protect your logins.

Firefox stores your personal data and settings in a profile folder. Learn what information it contains and how to find your profile. Password Manager · Troubleshooting Information · Restore bookmarks from...

Your Mozilla account and Firefox Sync allow you to save and sync your logins, as well as let you know if any of your passwords are ...

When you click Remember Password, the next time you visit the website, Firefox will automatically log you in to the website. A cookie is a piece ... Firefox password management · Cookies

Firefox has a password management feature to store usernames and passwords for logging in to websites. Learn why logins might not be saved.

Firefox securely stores your usernames and passwords for accessing websites, automatically fills them in for you the next time you visit a website, and lets you manage your stored logins with its built-in password management feature.

I am hoping there is a history of generated passwords somewhere, like in other password management systems, that I'm not seeing.

You would be better off to just export your passwords to a CSV file and then import them when you reinstall.