First, excuse me if I am making a wrong assumptions here. I assume you have Thunderbird 78 installed via the Ubuntu package manager and you want to upgrade to Thunderbird 91.
There are, at least, five ways, in principle:
Remove the apt version, and install the Thunderbird 91 snap, by choosing the "candidate" channel instead of "stable". This is a very safe way to upgrade, and recommended.
Find a PPA for Thunderbid 91. I could not find one, and I don't recommend PPAs typically.
Use the downloaded tar-archive from the Thunderbird website. I don't think the "update" is a program you are supposed to run, you should follow the instructions here: https://support.mozilla.org/en-US/kb/installing-thunderbird-linux
Remove Thunderbird 78 with
apt, and use the appimage version of Thunderbird 91.
Yet another alternative is a flatpak, available at https://flathub.org/apps/details/org.mozilla.Thunderbird
I know the instructions for the Mozilla tarball update are outdated, but should still work. It is up to you to place the extracted tar-archive to a place that is convenient for you. I personally would put it in ~/thunderbid and have a symbolic link to the thundebird binary at ~/bin.
You should either a) remove the old Thunderbird 78 via apt/package manager or b) at least make sure you don't accidentally run the old version by creating custom launchers for the new version and setting up your path correctly. I would remove the old Thunderbird completely. Mixing the two versions might lead to some serious weirdness.