feat(notifications): honor chat mute in web realtime alerts

tests/test_chat_message_flow.py

@@ -135,6 +135,37 @@ async def test_delete_saved_messages_chat_clears_messages_but_keeps_chat(client,
     assert messages_after_delete.json() == []
 
 
+async def test_chat_list_includes_notification_muted_flag(client, db_session):
+    u1 = await _create_verified_user(client, db_session, "muted_flag_u1@example.com", "muted_flag_u1", "strongpass123")
+    u2 = await _create_verified_user(client, db_session, "muted_flag_u2@example.com", "muted_flag_u2", "strongpass123")
+
+    me_u2 = await client.get("/api/v1/auth/me", headers={"Authorization": f"Bearer {u2['access_token']}"})
+    u2_id = me_u2.json()["id"]
+
+    create_chat_response = await client.post(
+        "/api/v1/chats",
+        headers={"Authorization": f"Bearer {u1['access_token']}"},
+        json={"type": ChatType.PRIVATE.value, "title": None, "member_ids": [u2_id]},
+    )
+    assert create_chat_response.status_code == 200
+    chat_id = create_chat_response.json()["id"]
+
+    mute_response = await client.put(
+        f"/api/v1/chats/{chat_id}/notifications",
+        headers={"Authorization": f"Bearer {u1['access_token']}"},
+        json={"muted": True},
+    )
+    assert mute_response.status_code == 200
+    assert mute_response.json()["muted"] is True
+
+    chats_response = await client.get("/api/v1/chats", headers={"Authorization": f"Bearer {u1['access_token']}"})
+    assert chats_response.status_code == 200
+    rows = chats_response.json()
+    row = next((item for item in rows if item["id"] == chat_id), None)
+    assert row is not None
+    assert row["muted"] is True
+
+
 async def test_private_chat_respects_contacts_only_policy(client, db_session):
     u1 = await _create_verified_user(client, db_session, "pm_u1@example.com", "pm_user_one", "strongpass123")
     u2 = await _create_verified_user(client, db_session, "pm_u2@example.com", "pm_user_two", "strongpass123")