Improve performance of fetching the state domain (#38653)

Pre calc domain when an entity id created to avoid
having to call the property method which had to call
split_entity_id every time. If there are a lot of
zone related automations, async_active_zone can call
async_entity_ids frequently which results in 100000s
of split_entity_id via the domain property every
second.

homeassistant/core.py

@@ -759,6 +759,7 @@ class State:
     last_changed: last time the state was changed, not the attributes.
     last_updated: last time this object was updated.
     context: Context in which it was created
+    domain: Domain of this state.
     """
 
     __slots__ = [
@@ -768,6 +769,7 @@ class State:
         "last_changed",
         "last_updated",
         "context",
+        "domain",
     ]
 
     def __init__(
@@ -801,11 +803,7 @@ class State:
         self.last_updated = last_updated or dt_util.utcnow()
         self.last_changed = last_changed or self.last_updated
         self.context = context or Context()
-
-    @property
-    def domain(self) -> str:
-        """Domain of this state."""
-        return split_entity_id(self.entity_id)[0]
+        self.domain = split_entity_id(self.entity_id)[0]
 
     @property
     def object_id(self) -> str: