The tab groups work by sandboxing a site to a specific one. Once you have it set up, every time you go to a site it’ll open in the correct tab group. Each tab group has it’s own seperate cookies.

If it’s the same website with multiple different logins you’re using though then yeah, this wouldn’t help at all.

Depending what exactly the OP needs, they may even be able to do it just using multi-account containers (sandboxed tab groups) in Firefox.

I only listen to albums (I have zero playlists) and I just double click on an album in Strawberry to listen to it.