Refactor integration startup time to show wall clock time (#113707)

* Refactor setup time tracking to exclude time waiting on other operations

We now exclude the import time and th time waiting on
base platforms to setup from the setup times

* tweak

* tweak

* tweak

* tweak

* adjust

* fixes

* fixes

* preen

* preen

* tweak

* tweak

* adjust

* tweak

* reduce

* do not count integrtion platforms against their parent integration

* handle legacy tts platforms

* stt as well

* one more wait

* use the same pattern in all the legacy

* fix tts and stt legacy

* fix

* fix

* reduce

* preen

* entity comp does not wait for platforms

* scene blocks as well

* fix test

* test fixes

* coverage

* coverage

* coverage

* fix test

* Update tests/test_setup.py

Co-authored-by: Martin Hjelmare <marhje52@gmail.com>

* Update tests/test_setup.py

Co-authored-by: Martin Hjelmare <marhje52@gmail.com>

* Update homeassistant/setup.py

Co-authored-by: Martin Hjelmare <marhje52@gmail.com>

* strip

* strip WAIT_PLATFORM_INTEGRATION

* strip WAIT_PLATFORM_INTEGRATION

* strip WAIT_PLATFORM_INTEGRATION

* strip WAIT_PLATFORM_INTEGRATION

* remove complexity

* Apply suggestions from code review

* no longer works that way

* fixes

* fixes

* fixes

---------

Co-authored-by: Martin Hjelmare <marhje52@gmail.com>

tests/test_bootstrap.py

@@ -14,7 +14,7 @@ from homeassistant import bootstrap, loader, runner
 import homeassistant.config as config_util
 from homeassistant.config_entries import HANDLERS, ConfigEntry
 from homeassistant.const import SIGNAL_BOOTSTRAP_INTEGRATIONS
-from homeassistant.core import HomeAssistant, async_get_hass, callback
+from homeassistant.core import CoreState, HomeAssistant, async_get_hass, callback
 from homeassistant.exceptions import HomeAssistantError
 from homeassistant.helpers.dispatcher import async_dispatcher_connect
 from homeassistant.helpers.typing import ConfigType
@@ -869,6 +869,9 @@ async def test_empty_integrations_list_is_only_sent_at_the_end_of_bootstrap(
     hass: HomeAssistant,
 ) -> None:
     """Test empty integrations list is only sent at the end of bootstrap."""
+    # setup times only tracked when not running
+    hass.set_state(CoreState.not_running)
+
     order = []
 
     def gen_domain_setup(domain):