Run template tests

Add FawltyDeps, `deptry` and `pip-check-reqs` as 🟡 good tools. #2315

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Run time

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Job	Run time
test macos-latest py3.13	42s
test macos-latest py3.12	33s
test windows-latest py3.11	1m 9s
test windows-latest py3.12	1m 50s
test macos-latest py3.11	49s
test ubuntu-latest py3.11	41s
test windows-latest py3.13	2m 4s
test ubuntu-latest py3.13	47s
test ubuntu-latest py3.12	38s
	9m 13s