Avoid duplicate timestamp conversions for websocket api and recorder (#108144)

* Avoid duplicate timestamp conversions for websocket api and recorder

We convert the time from datetime to timestamps one per
open websocket connection and the recorder for every
state update. Only do the conversion once since its
~30% of the cost of building the state diff

* more

* two more

* two more in live history

tests/test_core.py

@@ -625,6 +625,14 @@ def test_event_eq() -> None:
     assert event1.as_dict() == event2.as_dict()
 
 
+def test_event_time_fired_timestamp() -> None:
+    """Test time_fired_timestamp."""
+    now = dt_util.utcnow()
+    event = ha.Event("some_type", {"some": "attr"}, time_fired=now)
+    assert event.time_fired_timestamp == now.timestamp()
+    assert event.time_fired_timestamp == now.timestamp()
+
+
 def test_event_json_fragment() -> None:
     """Test event JSON fragments."""
     now = dt_util.utcnow()
@@ -2453,6 +2461,23 @@ async def test_state_change_events_context_id_match_state_time(
     )
 
 
+def test_state_timestamps() -> None:
+    """Test timestamp functions for State."""
+    now = dt_util.utcnow()
+    state = ha.State(
+        "light.bedroom",
+        "on",
+        {"brightness": 100},
+        last_changed=now,
+        last_updated=now,
+        context=ha.Context(id="1234"),
+    )
+    assert state.last_changed_timestamp == now.timestamp()
+    assert state.last_changed_timestamp == now.timestamp()
+    assert state.last_updated_timestamp == now.timestamp()
+    assert state.last_updated_timestamp == now.timestamp()
+
+
 async def test_state_firing_event_matches_context_id_ulid_time(
     hass: HomeAssistant,
 ) -> None: