fix: resolve three high-impact community bugs (#5819, #6893, #3388) (#7881)

Matrix gateway: fix sync loop never dispatching events (#5819)
- _sync_loop() called client.sync() but never called handle_sync()
  to dispatch events to registered callbacks — _on_room_message was
  registered but never fired for new messages
- Store next_batch token from initial sync and pass as since= to
  subsequent incremental syncs (was doing full initial sync every time)
- 17 comments, confirmed by multiple users on matrix.org

Feishu docs: add interactive card configuration for approvals (#6893)
- Error 200340 is a Feishu Developer Console configuration issue,
  not a code bug — users need to enable Interactive Card capability
  and configure Card Request URL
- Added required 3-step setup instructions to feishu.md
- Added troubleshooting entry for error 200340
- 17 comments from Feishu users

Copilot provider drift: detect GPT-5.x Responses API requirement (#3388)
- GPT-5.x models are rejected on /v1/chat/completions by both OpenAI
  and OpenRouter (unsupported_api_for_model error)
- Added _model_requires_responses_api() to detect models needing
  Responses API regardless of provider
- Applied in __init__ (covers OpenRouter primary users) and in
  _try_activate_fallback() (covers Copilot->OpenRouter drift)
- Fixed stale comment claiming gateway creates fresh agents per message
  (it caches them via _agent_cache since the caching was added)
- 7 comments, reported on Copilot+Telegram gateway

tests/gateway/test_matrix.py

@@ -1043,20 +1043,28 @@ class TestMatrixSyncLoop:
             call_count += 1
             if call_count >= 1:
                 adapter._closing = True
-            return {"rooms": {"join": {"!room:example.org": {}}}}
+            return {"rooms": {"join": {"!room:example.org": {}}}, "next_batch": "s1234"}
 
         mock_crypto = MagicMock()
         mock_crypto.share_keys = AsyncMock()
 
+        mock_sync_store = MagicMock()
+        mock_sync_store.get_next_batch = AsyncMock(return_value=None)
+        mock_sync_store.put_next_batch = AsyncMock()
+
         fake_client = MagicMock()
         fake_client.sync = AsyncMock(side_effect=_sync_once)
         fake_client.crypto = mock_crypto
+        fake_client.sync_store = mock_sync_store
+        fake_client.handle_sync = MagicMock(return_value=[])
         adapter._client = fake_client
 
         await adapter._sync_loop()
 
         fake_client.sync.assert_awaited_once()
         mock_crypto.share_keys.assert_awaited_once()
+        fake_client.handle_sync.assert_called_once()
+        mock_sync_store.put_next_batch.assert_awaited_once_with("s1234")
 
 
 class TestMatrixEncryptedSendFallback: