Set sso_hint cookie on login, clear on logout

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

bp/auth/routes.py

@@ -196,11 +196,19 @@ def register(url_prefix="/auth"):
         qsession[SESSION_USER_KEY] = user_id
 
         redirect_url = pop_login_redirect_target()
-        return redirect(redirect_url, 303)
+        resp = redirect(redirect_url, 303)
+        resp.set_cookie(
+            "sso_hint", "1",
+            domain=".rose-ash.com", max_age=30 * 24 * 3600,
+            secure=True, samesite="Lax", httponly=True,
+        )
+        return resp
 
     @auth_bp.post("/logout/")
     async def logout():
         qsession.pop(SESSION_USER_KEY, None)
-        return redirect(federation_url("/"))
+        resp = redirect(federation_url("/"))
+        resp.delete_cookie("sso_hint", domain=".rose-ash.com", path="/")
+        return resp
 
     return auth_bp