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You shouldn’t need to log in, unless you’re adding a service connection, which will be your personal account data, and stay on their system when you leave.
But you can play all the music using their Sonos all you want.
It shouldn’t. You’re connecting to their speakers, which have their streaming services associated with them, not yours. Your account data is stored on your speakers, not in the controller or in a cloud system. You get access to the data stored on the speakers you are connected to.
When I’m at my friend’s house, I use AirPlay 2 to send my stored music to their Sonos speakers, or just use their Spotify playlists.