Am I being overly paranoid?
Yes, simply connecting to the Tor network is not a sketchy thing and browsing the clearnet using Tor is a smart way to preserve your privacy if you aren't in a hurry for your pages to load.
I used to browse the clearnet with Tor regularly but eventually I decided it was overkill and stopped (Tor really is slow a lot of the time so it isn't always a walk in the park).