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

homeassistant/core.py

@@ -1077,6 +1077,11 @@ class Event:
         if not context.origin_event:
             context.origin_event = self
 
+    @cached_property
+    def time_fired_timestamp(self) -> float:
+        """Return time fired as a timestamp."""
+        return self.time_fired.timestamp()
+
     @cached_property
     def _as_dict(self) -> dict[str, Any]:
         """Create a dict representation of this Event.
@@ -1445,6 +1450,16 @@ class State:
             "_", " "
         )
 
+    @cached_property
+    def last_updated_timestamp(self) -> float:
+        """Timestamp of last update."""
+        return self.last_updated.timestamp()
+
+    @cached_property
+    def last_changed_timestamp(self) -> float:
+        """Timestamp of last change."""
+        return self.last_changed.timestamp()
+
     @cached_property
     def _as_dict(self) -> dict[str, Any]:
         """Return a dict representation of the State.
@@ -1526,12 +1541,12 @@ class State:
             COMPRESSED_STATE_STATE: self.state,
             COMPRESSED_STATE_ATTRIBUTES: self.attributes,
             COMPRESSED_STATE_CONTEXT: context,
-            COMPRESSED_STATE_LAST_CHANGED: dt_util.utc_to_timestamp(self.last_changed),
+            COMPRESSED_STATE_LAST_CHANGED: self.last_changed_timestamp,
         }
         if self.last_changed != self.last_updated:
-            compressed_state[COMPRESSED_STATE_LAST_UPDATED] = dt_util.utc_to_timestamp(
-                self.last_updated
-            )
+            compressed_state[
+                COMPRESSED_STATE_LAST_UPDATED
+            ] = self.last_updated_timestamp
         return compressed_state
 
     @cached_property