Refactor User attribute caching to be safer and more efficient (#96723)

* Cache construction of is_admin

This has to be checked for a lot of api calls and the websocket
every time the call is made

* Cache construction of is_admin

This has to be checked for a lot of api calls and the websocket
every time the call is made

* Cache construction of is_admin

This has to be checked for a lot of api calls and the websocket
every time the call is made

* modernize

* coverage

* coverage

* verify caching

* verify caching

* fix type

* fix mocking

tests/components/api/test_init.py

@@ -684,6 +684,8 @@ async def test_get_entity_state_read_perm(
 ) -> None:
     """Test getting a state requires read permission."""
     hass_admin_user.mock_policy({})
+    hass_admin_user.groups = []
+    assert hass_admin_user.is_admin is False
     resp = await mock_api_client.get("/api/states/light.test")
     assert resp.status == HTTPStatus.UNAUTHORIZED