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/components/config/test_scene.py

@@ -19,6 +19,7 @@ from tests.typing import ClientSessionGenerator
 async def setup_scene(hass, scene_config):
     """Set up scene integration."""
     assert await async_setup_component(hass, "scene", {"scene": scene_config})
+    await hass.async_block_till_done()
 
 
 @pytest.mark.parametrize("scene_config", ({},))