Refactor integration testing #472

Job	Run time
pre-commit	25s
fast-tests	1m 0s
integration-tests-examples (ubuntu-22.04)	39s
integration-tests-aspect (ubuntu-22.04)	4m 42s
integration-tests-examples (macos-12)	1m 36s
integration-tests-apply-fixes (ubuntu-22.04)	3m 42s
integration-tests-aspect (macos-12)	10m 58s
integration-tests-examples (windows-2022)	6m 17s
integration-tests-apply-fixes (macos-12)	9m 41s
integration-tests-aspect (windows-2022)	9m 11s
integration-tests-apply-fixes (windows-2022)	21m 52s
	1h 10m 3s

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