Sync async_test_home_assistant with core #4036

Job	Run time
Preflight	1s
Check integration hacs/integration with HACS Action (local)	1m 6s
Check plugin piitaya/lovelace-mushroom with HACS Action (local)	1m 22s
With hassfest	1m 41s
With HACS Action	27s
Check integration hacs/integration with HACS data generation	45s
Check plugin piitaya/lovelace-mushroom with HACS data generation	46s
With Home Assistant stable	1m 26s
With Home Assistant beta	1m 23s
With Home Assistant dev	1m 30s
With Home Assistant 2023.6.0	1m 19s
Trigger Discord notification when jobs fail	1s
	11m 47s

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