Do I get this right that you still want to support a version using the old API for Thunderbird users parralel to the new WebExtension version for Firefox (two "branches")?
If so, then I think this should work:
Thunderbird users will always get the latest compatible version and Firefox users will always get the absolutely latest version.
So updating with a version that uses the WebExtension API won't affect Thunderbird users at all.
Updating with a version that works in Thunderbird however would overwrite the add-on for Firefox users too, so simply "cover" that with another WebExtension update.
Oh, and you will always need to get both versions approved (Updating while you still have an update pending usually disables the pending version).
So you should wait for the first update to be approved, disable it yourself immediately (so it won't get shipped to users), submit the 2nd update and, once that is approved, re-enable the first update.
Ok, this really isn't a nice workflow ...