Fix setup timings when config entry platform loads are not awaited (#113959)

* Move setup time logging into the context manager

We were fetching the time twice but since the context
manager already has the timing, move it there

* remove log setup assertions from integration test

* tweak logging to give us better data for tracking issues

* redundant

* adjust

* preen

* fixes

* adjust

* make api change internal so nobody uses it

* coverage

* fix test

* fix more tests

* coverage

* more tests assuming internal calls

* fix more

* adjust

* adjust

* fix axis tests

* fix broadlink -- it does not call async_forward_entry_setup

* missed some

* remove useless patch

* rename, detect it both ways

* clear

* debug

* try to fix

* handle phase finishing out while paused

* where its set does not need to know its late as that is an implemenation detail of setup

* where its set does not need to know its late as that is an implemenation detail of setup

* tweak

* simplify

* reduce complexity

* revert order change as it makes review harder

* revert naming changes as it makes review harder

* improve comment

* improve debug

* late dispatch test

* test the other way as well

* Update setup.py

* Update setup.py

* Update setup.py

* simplify

* reduce

tests/components/tts/test_legacy.py

@@ -148,6 +148,7 @@ async def test_service_without_cache_config(
 
     with assert_setup_component(1, DOMAIN):
         assert await async_setup_component(hass, DOMAIN, config)
+        await hass.async_block_till_done()
 
     await hass.services.async_call(
         DOMAIN,