After using containers to isolate my Google activity in a similar fashion, I can confirm Google at least does. I see recommendations to watch other videos from the same channels I watch on YouTube in my Google container if I end up on YouTube in my normal browsing container.
Are you logged out of (or never logged in to) any of the Google properties/platforms in these two modes? If yes, then Google's behavior here doesn't match user expectations and is tainted.
There is one silver lining in carrier grade NAT. combine that and all facebook ends up with is you are one of a few hundred firefox users in some geographical area.
Not necessarily! Other fingerprinting details can surface identity even when user agent and IP are unreliable. If you've got a specific screen resolution, you're tagged. If you've got a specific version of some piece of software (Flash, for instance) you're tagged.
more than that, theres a bunch of sites that buy your email address/phone number from companies, which then provide matching across browsers/devices/containers/etc which they sell to others. All you need to do is log into one on each and the cookies get linked and they know its the same person.