I think I can confidently assume that despite not providing IP or accurate location data, there are enough features in the data for their partners to fingerprint individuals. Might require a lot more work, but when advertisers go out of their way to identify individuals based on their browser/os/hardware settings, they'll attempt to do it on just about anything they could get their hands on.

I wonder how containers affect this behavior? Since the same history seems to pop up regardless of which container I'm in, I wonder if this effectively makes containers permeable?