test(config-flow): drive the menus, pin the tables, probe real HA

The flow tests drove `async_step_init` as if it were the one form, so they
had to learn the menu: a shared helper picks the sub-screen that owns a
payload's keys out of the flow's own `menu_options` (no test re-implements
the routing), and a `save=True` flag walks to "Save and close" so the
assertions read as they did before.

New coverage for this task:

- the menu offers every sub-screen and every row has a handler named
  after it, with the rendered step_id equal to the row id (the invariant
  real HA enforces and the first draft broke);
- edits on one sub-screen are not lost by another, and a page that is
  never saved never writes the entry;
- the apps table: add / edit / remove a row, the icon column round-trips,
  the empty state renders without data, a blank field clears the map, and
  the suggested value is TEXT (the `[object Object]` layer);
- a receiver the selector offers `switch` for, stored and pre-filled;
- the setup menu's rows, their handlers and a connection+receiver merge.

tests/test_config_flow_real_ha.py is new and is the empirical half: it
drives the real `FlowManager`, real probatio validation and the real
frontend serialiser (`to_field_list` + `cv.custom_serializer`) — the call
the HTTP flow view makes — so the menu dispatch, the cleared-selector
shapes and the wire serialisation are established rather than assumed.
It skips when homeassistant is absent; CI runs it with:

    uvx --with homeassistant --with adb-shell pytest tests/test_config_flow_real_ha.py

53 of the stub tests and 11 of the real-HA ones fail on the pre-fix tree.

tests/test_config_flow_pairing.py

@@ -69,6 +69,17 @@ def _install_import_stubs() -> None:
         def async_show_form(self, *, step_id, data_schema=None, errors=None):
             return _form(step_id, errors or {})
 
+        def async_show_menu(self, *, step_id, menu_options, sort=False,
+                            description_placeholders=None, errors=None):
+            # t56: the real MENU result shape; the flow manager dispatches the
+            # chosen `next_step_id` to `async_step_<choice>(None)`.
+            return {
+                "type": "menu",
+                "step_id": step_id,
+                "menu_options": list(menu_options),
+                "errors": dict(errors or {}),
+            }
+
         def async_create_entry(self, *, title, data, options=None):
             return {"type": "create_entry", "title": title, "data": data,
                     "options": options}
@@ -212,6 +223,9 @@ async def test_pairing_submit_uses_declared_signature(mocked_test_connect):
     mocked_test_connect.assert_awaited_once_with(
         "shield.local", 5555, _KEY_PATH
     )
+    # t56: the pairing hands over to the setup menu; Finish creates the entry
+    assert result["type"] == "menu"
+    result = await flow.async_step_finish(None)
     assert result["type"] == "create_entry"