Since you brought up logging out and in, remember that Firefox Containers are very useful for things you wanna let logged in all the time (e.g., Facebook, maybe Google) so their tracking gets a little worse because your cookies are more isolated.
My preferred anti-tracking setup is Firefox with the Multi-Account Containers and the Temporary Containers addons (and uBlock Origin of course.)
Multi-Account Contaners lets me set up permanent containers for (groups of) sites I want to stay logged in to. I check the "always open this site in <container name>" box.
Temporary Containers is set up to open new sites (on middle / control click) in new, temporary containers. These containers work like private browsing windows, but store their data for 10 minutes after being closed. So undo close tab works, history works, but each new site is in its own container. And 10 minutes after its closed (or when the browser as a whole closes) all the cookies get deleted.
I ran Privacy Badger for a while, but I have never actually seen it do anything. Not sure I messed up something, or if it was due to me already having an aggressive block list on uBlock Origin that left PB with nothing to do.
An aggressive block list could do it. Privacy Badger "learns" what is tracking you, so it does take a little bit to start being effective when you first start using it. It caches 34 trackers on theverge.com with uBlock Origin turned off for me, and 9 with uBlock Origin turned on.
My preferred anti-tracking adds Cookie Auto delete [0] to this. In the HN container, I keep HN cookies. Anything opened from HN will stay in the HN container and non-HN sites get cookies deleted shortly.
One thing that turns me off using Firefox Containers in earnest is that they are not integrated into Firefox Sync and nor does there appear to be a way to backup the URLs/containers as with other extensions - so I end up having to rebuild the containers on another machine or when I need to delete a buggy profile.
That's a great change. Containers are one of the things that made me move back from Chrome, it just feels far more useful to me to mix different contexts in one window than having to run entirely separate browser profiles as I had in Chrome. The one thing that prevented me from creating more elaborate container setups was the lack of sync, it just gets too annoying to set that kind of stuff up repeatedly. But with sync I'll probably look at creating more fine-grained containers than the basic work/personal setup I have right now, e.g. separating out Google in a separate container.