test: cover InlineQueryHandler in lazy-install rebind and handler-count contracts

The lazy-install placeholder test failing mid-run also left the adapter
module's ParseMode as None, cascading into test_telegram_thread_fallback
failures in the same CI process — all downstream of the same root.

tests/gateway/test_gateway_platform_event_hook.py

@@ -672,13 +672,14 @@ class TestRegisterHandlers:
         app = MagicMock()
         a._register_handlers(app)
 
-        # Five core handlers (default group, no group kwarg) plus the
-        # gateway_platform_event observer alone in group 99, so it observes
-        # alongside rather than displacing the core handlers.
+        # Six core handlers (default group, no group kwarg — incl. the
+        # inline command picker) plus the gateway_platform_event observer
+        # alone in group 99, so it observes alongside rather than
+        # displacing the core handlers.
         calls = app.add_handler.call_args_list
-        assert len(calls) == 6
+        assert len(calls) == 7
         assert len([c for c in calls if c.kwargs.get("group") == 99]) == 1
-        assert len([c for c in calls if not c.kwargs]) == 5
+        assert len([c for c in calls if not c.kwargs]) == 6
 
     def test_rebuild_re_registers_observer(self):
         """A second call on a fresh app (e.g. a future rebuild) re-registers
@@ -690,7 +691,7 @@ class TestRegisterHandlers:
         a._register_handlers(first_app)
         a._register_handlers(rebuilt_app)  # the rebuild path
 
-        assert rebuilt_app.add_handler.call_count == 6
+        assert rebuilt_app.add_handler.call_count == 7
         assert len(self._observer_calls(rebuilt_app)) == 1
 
     def test_transient_init_rebuild_uses_shared_registration(self, monkeypatch):

tests/gateway/test_telegram_lazy_install_typehandler.py

@@ -47,6 +47,7 @@ def fake_telegram_sdk(monkeypatch):
             "Application",
             "CommandHandler",
             "CallbackQueryHandler",
+            "InlineQueryHandler",
             "MessageHandler",
             "TypeHandler",
             "HTTPXRequest",
@@ -69,6 +70,7 @@ def fake_telegram_sdk(monkeypatch):
         "Application",
         "CommandHandler",
         "CallbackQueryHandler",
+        "InlineQueryHandler",
         "MessageHandler",
         "TypeHandler",
     ):
@@ -119,6 +121,7 @@ def test_lazy_install_rebinds_every_placeholder(monkeypatch, fake_telegram_sdk):
         "Application",
         "CommandHandler",
         "CallbackQueryHandler",
+        "InlineQueryHandler",
         "TelegramMessageHandler",
         "TypeHandler",
         "ContextTypes",