Better describe your issue. Sounds like you're going from a old computer to a new computer. If so, just use Sync.

FYI... SYNC IS NOT A DATA BACKUP SERVICE Sync info... https://support.mozilla.org/en-US/kb/how-do-i-set-sync-my-computer https://support.mozilla.org/en-US/kb/how-do-i-choose-what-information-sync-firefox https://www.mozilla.org/en-US/firefox/features/sync/ https://hacks.mozilla.org/2018/11/firefox-sync-privacy/ Sync is not a backup tool but it is a good sync/transfer/move tool https://support.mozilla.org/en-US/forums/contributors/707681

how to update firefox from extended release to new updates on new computer

Do you want to move from the Firefox 128 series to the Firefox 140 series? At some point, this should happen automatically, but I'm not sure when. If you do want to do it now, you should be able to download a DMG file and install the app that way. As a Windows person, I don't have personal experience with that, but see:

• How to download and install Firefox on Mac
• https://www.mozilla.org/firefox/all/desktop-esr/