Nope; different profiles.
The console that I want anyone in the house to have access to Gold/GP is set as the 'Home' console in settings (have you done that? If not, you can read the support article
here). The other console, that only I play, is obviously not set as the 'Home' console but picks up my game licences/Gold/Game Pass via my Gamertag when I log into that.
With the above, I can be on my Series X upstairs, and my wife or kids can sign in with their own gamertags on the Series S downstairs and play any game I own, or have access to via Game Pass (it also worked this way one Xbox One, we had an OG Xbox One downstairs and a One S upstairs).