What would be the better option for privacy. Logging into my windows partition and using zoom just for class logging right back out or install zoom on my linux partition?
That is no longer necessary with Dynamic State Partitioning. Every top level domain is automatically given its own container, essentially. The extension is really only useful for logging into sites on two accounts simultaneously.
Sort of. There are still tricks that can be used like redirecting between sites to "sync" their states. Container tabs can still be useful because if they do this then the sites will all be "fresh" to that container and not shared between websites. But for the most part yes, different sites have limited ability to track you other than things like fingerprinting and IP address.