Add and fix type hints (#36501)

* Fix exceptions.Unauthorized.permission type

* Use auth.permission consts more

* Auth typing improvements

* Helpers typing improvements

* Calculate self.state only once

homeassistant/core.py

@@ -79,6 +79,7 @@ from homeassistant.util.unit_system import IMPERIAL_SYSTEM, METRIC_SYSTEM, UnitS
 
 # Typing imports that create a circular dependency
 if TYPE_CHECKING:
+    from homeassistant.auth import AuthManager
     from homeassistant.config_entries import ConfigEntries
     from homeassistant.components.http import HomeAssistantHTTP
 
@@ -174,6 +175,7 @@ class CoreState(enum.Enum):
 class HomeAssistant:
     """Root object of the Home Assistant home automation."""
 
+    auth: "AuthManager"
     http: "HomeAssistantHTTP" = None  # type: ignore
     config_entries: "ConfigEntries" = None  # type: ignore