Problem: Tor freezes / lags after update to v13.0.6

I had the same issue. Long story short, I figured out downgrading Tampermonkey does the trick. I did download version 4.19.0 from the mozilla page and installed it via Extensions → Gear Icon → Install Add-On From File. Tor Browser is still the latest version. I did disable the auto update for Tampermonkey.

I did not have to do any backups of anything, everything went smooth, but prob create a copy of your Tor Browser first in case you should have issues with your Tampermonkey scripts.

https://addons.mozilla.org/en-US/firefox/addon/tampermonkey/versions