Persist user login/logout audit in ncue_user

Add first_login_at and last_logout_at, ensure table exists at runtime, upsert user on /api/auth/sync, and record logout via /api/auth/logout from the client.

Co-authored-by: Cursor <cursoragent@cursor.com>

db/schema.sql

@@ -15,7 +15,9 @@ BEGIN
       name           text,
       picture        text,
       provider       text,
+      first_login_at timestamptz,
       last_login_at  timestamptz,
+      last_logout_at timestamptz,
       can_manage     boolean NOT NULL DEFAULT false,
       created_at     timestamptz NOT NULL DEFAULT now(),
       updated_at     timestamptz NOT NULL DEFAULT now()
@@ -25,3 +27,7 @@ BEGIN
   END IF;
 END $$;
 
+-- Backward-compatible migration (if table already exists)
+ALTER TABLE public.ncue_user ADD COLUMN IF NOT EXISTS first_login_at timestamptz;
+ALTER TABLE public.ncue_user ADD COLUMN IF NOT EXISTS last_logout_at timestamptz;
+