Fix cancellation leaking upward from the timeout util #219659

Job	Run time
Collect information & changes data	14s
Prepare dependencies (3.12)	11s
Prepare pre-commit base	17s
Check Dockerfile	13s
Check Dockerfile.dev	13s
Check script/hassfest/docker/Dockerfile	12s
Check all requirements	22s
Check hassfest	43s
Check pylint on tests	6m 2s
Check pylint	8m 40s
Audit licenses	0s
Check mypy	48s
Split tests for full run Python 3.12	6m 24s
Check ruff	11s
Check other linters	59s
Check ruff-format	11s
Run postgres:12.14 tests Python 3.12	10m 28s
Run postgres:15.2 tests Python 3.12	11m 18s
Run mariadb:10.3.32 tests Python 3.12	10m 18s
Run tests Python ${{ matrix.python-version }} (${{ matrix.group }})	0s
Run mariadb:10.6.10 tests Python 3.12	10m 6s
Run mariadb:10.10.3 tests Python 3.12	9m 20s
Run mariadb:10.11.2 tests Python 3.12	10m 12s
Run mysql:8.0.32 tests Python 3.12	13m 1s
Upload test coverage to Codecov (partial suite)	0s
Run tests Python 3.12 (1)	6m 9s
Run tests Python 3.12 (2)	9m 34s
Run tests Python 3.12 (3)	8m 48s
Run tests Python 3.12 (4)	13m 1s
Run tests Python 3.12 (5)	12m 10s
Run tests Python 3.12 (6)	11m 37s
Run tests Python 3.12 (7)	12m 48s
Run tests Python 3.12 (8)	13m 0s
Run tests Python 3.12 (9)	11m 7s
Run tests Python 3.12 (10)	9m 52s
Upload test coverage to Codecov (full suite)	1s
	3h 28m 30s

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