I get session data without cookies

I've been testing the supabase for a while and the auth system confusing me a bit.
I sign in the user on the server with supabaseClient.auth.signIn({email, password})
And then when I do supabaseClient.auth.session() on the server upon page request, I get the session. However, there is no cookie or local storage set on the browser.

Then when I visit my dev server's address on another browser (Safari) and I get the session. I even get the session on incognito mode.

So, how does this actually work? I don't even pass anything to supabaseClient.auth.session() This must be coming from the supabase server, but then how can I sign-in multiple users? I am a bit confused
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