Adjust recorder LRU cache to align with the number of entities (#88350)

* Adjust size of recorder LRU based on number of entities

If there are a large number of entities the cache would
get thrashed as there were more state attributes being
recorded than the size of the cache. This meant we had
to go back to the database to do lookups frequently when
an instance has more than 2048 entities that change
frequently

* add a test

* do not actually record 4096 states

* patch target

* patch target

tests/components/recorder/test_init.py

@@ -2075,3 +2075,18 @@ async def test_excluding_attributes_by_integration(
     expected = _state_with_context(hass, entity_id)
     expected.attributes = {"test_attr": 5}
     assert state.as_dict() == expected.as_dict()
+
+
+async def test_lru_increases_with_many_entities(
+    recorder_mock: Recorder, hass: HomeAssistant
+) -> None:
+    """Test that the recorder's internal LRU cache increases with many entities."""
+    # We do not actually want to record 4096 entities so we mock the entity count
+    mock_entity_count = 4096
+    with patch.object(
+        hass.states, "async_entity_ids_count", return_value=mock_entity_count
+    ):
+        async_fire_time_changed(hass, dt_util.utcnow() + timedelta(minutes=10))
+        await hass.async_block_till_done()
+
+    assert recorder_mock._state_attributes_ids.get_size() == mock_entity_count * 2