Add async start hook to ExtensionApp API #3000

Job	Run time
build (ubuntu-latest, 3.8)	5m 51s
Test Examples	55s
build (ubuntu-latest, 3.11)	6m 5s
Test Docs	1m 9s
build (windows-latest, 3.8)	12m 56s
build (windows-latest, 3.11)	10m 59s
Check Links	4m 44s
build (macos-latest, 3.8)	5m 25s
check_release	1m 56s
build (macos-latest, 3.11)	4m 51s
build (windows-latest, 3.9)	14m 1s
integration_check (ubuntu-latest, 3.8)	2m 16s
build (ubuntu-latest, pypy-3.8)	12m 35s
integration_check_pypy	2m 49s
build (macos-latest, 3.10)	4m 52s
integration_check (ubuntu-latest, 3.9)	2m 13s
integration_check (ubuntu-latest, 3.10)	2m 10s
build (ubuntu-latest, 3.12)	6m 34s
Make SDist	49s
Test Lint	40s
integration_check (ubuntu-latest, 3.11)	2m 25s
Test Minimum Versions	4m 58s
Test Prereleases	4m 36s
Install from SDist and Test	4m 31s
coverage	0s
tests_check	4s
	2h 0m 24s

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