Is there a way to remove previous session without hard refreshing (sveltekit and Supabase)

Question

im practicing authentication at the moment with sveltekit and Supabase

RLS is on and one of the issues im having is after i log out, and i sign in with another email, i can see the info from the previous session and when i hard refresh, then i see the correct data. Im not sure how to fix this

in my store

export const user = readable(null, (set) => {
    set(supabase.auth.user());
    const unsubscribe = supabase.auth.onAuthStateChange((_, session) => {
        session ? set(session.user) : set(null);
    });
    return () => {
        unsubscribe.data.unsubscribe();
    };
});