Like some other users, my TB (v134.0.1) was still slow to find and download my emails. Even though TB was lightning fast for years before this slowness epidemic started, I decided to fiddle with settings. I tried various things that seemed logical, but had no success until I changed the "Connection Security" in "Server Settings" for all my accounts from SSL/TLS to STARTTLS. My guess is that the TB devs have changed the way it communicates with mail servers about security and some can't deal with it quickly enough!

Your mileage will likely vary, so make a note of your settings before changing anything and only ever change one type of setting at a time in only one account before doing a test. I hope this helps at least some users and reduces their frustration.