The only things TF logs are whatever you put in threads as they're stored in the DB.
As for cookies...The only cookies directly from TF are related to your login session.
Here's the objects stored in my current session, according to Chrome:
And here's the only things red flagged (blocked) by uBlock:
I don't have Privacy Badger installed at work, otherwise I'd post a screenshot of it's results as well.
Edit: Here's Privacy Badger. There's 2 additional domains under the "Don't seem to be tracking you" section, which are: