How to view a Mozilla Firefox saved password before it was updated?

Probably impossible. Maybe the affected website has a password reset function you could try?

Firefox 80+ has a logins-backup.json file in the profile folder that can be used in case of issues with logins.json or to undo an accidental delete/update of a password. You can check if you can find this logins-backup.json file in the profile folder or in a backup. You can open logins-backup.json in a Firefox tab to check if you can find records for the hostname of missing logins (hostname shows as plain text; username and password are encrypted).

Make sure to keep a backup of the current logins.json and logins-backup.json before replacing logins.json with logins-backup.json with Firefox closed.

You can use the button in "Help -> More Troubleshooting Information" (about:support) to go to the current Firefox profile folder or use the about:profiles page (Root directory).

• Help -> More Troubleshooting Information -> Profile Folder/Directory:
  Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

@cor-el, This was really good information. I found the profile directory using the page about:support. The following was my path:

C:\Users\user\AppData\Roaming\Mozilla\Firefox\Profiles\Base64String.default-release 

I searched for logins*.json in this path and found both files; however, they are both the same file. I suppose the backup keeps being updated with "logins.json". How is it going to help me in this situation? The way I found my old password was by using my old computer. I turned it on, turned off the internet by turning off the WiFi, then opened Firefox, and opened the page about:logins to find the old password.