With the updated code changes, I've created a new deployment version with new version number which I usually do to deploy my Gmail add-on. But this time, after deployment, when I'm doing authentication with the third party, I'm getting an error:
Library with identifier SetmoreForGmail is missing (perhaps it was deleted, or maybe you don't have read access?)

The error message you are getting is due to the fact that the library with the
SetmoreForGmailis missing.You just need to go to your project's libraries and (re)add it in order for the script to work as expected.
Reference