With several 10s of thousands of messages (~70 GB) in my accounts, I also had issues with TB using tons of disk space even when set to not copy messages locally. The issue was TB's global search index. If you disable global search indexing in your config, then manually delete the global-messages-db.sqlite file, you can free up those 10+ GB.
My fix for most annoyances was to copy mail locally, and run dovecot locally on the same box as TB (TB doesn't support standard maildir). I also added a wrapper script that does a VACUUM on all the sqlite dbs in the profile when starting TB.
I didn't realize how many sqlite files there are, I ran "find . -name *.sqlite", I see Chrome related files, cookie files, a file related to storage? Time to look for a new email client which is sad to say after all these years.
My fix for most annoyances was to copy mail locally, and run dovecot locally on the same box as TB (TB doesn't support standard maildir). I also added a wrapper script that does a VACUUM on all the sqlite dbs in the profile when starting TB.
With the above, TB has worked well for me.