> I am currently running Thunderbird from a subfolder in /Applications. Do I have to move it before updating?

If you installed Thunderbird using the default process, then it is in /Applications at an expected location, and there is no need to move it. Mine is in /Applications/Thunderbird.app/

> Before upgrading the OS, should I update Thunderbird to version 128 so that, after the OS upgrade, Thunderbird will then be updated from version 128 instead of version 115?

It is not necessary to update Thunderbird first.

When you do wish to change to 138 or newer, you can use https://support.mozilla.org/en-US/kb/thunderbird-release/, or stay on ESR. The choice is yours https://support.mozilla.org/en-US/kb/choosing-thunderbird-release-channel/

Thank you Mr. Mery. I’m pleased to know one can update from v115 directly to v138.

However, the location issue is confusing. I am indeed on the ESR channel (didn’t know that and don’t know how I got there). So, to change from ESR to Release, the instructions state,

“Visit the download website ...Run the downloaded file to install the monthly release into the same directory where the ESR is currently installed... If you previously installed Thunderbird ESR into a directory that is different from the default location, then you must do a custom installation to that directory.”

The foregoing instructions contradict the warning that TB must be installed in /Applications. As I said, my installation is in a subfolder of /Applications (been there for ages with no problem). Also, “Run the downloaded file to install” and “a custom installation” do not sound like dragging a file from a dmg. Perhaps that accounts for the different location requirements?

For Mac, yes, a subfolder of /Applications is correct.

> It is not necessary to update Thunderbird first.

This statement was meant to say it is not necessary to update TB before updating macOS. However, I'm not suggesting going from 115 that you skip 128 on the way to 138 (or 139).