Run template tests

Add FawltyDeps, `deptry` and `pip-check-reqs` as 🟡 good tools. #2314

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Run time

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Job	Run time
test macos-latest py3.11	56s
test ubuntu-latest py3.12	42s
test ubuntu-latest py3.11	40s
test macos-latest py3.12	37s
test macos-latest py3.13	40s
test ubuntu-latest py3.13	42s
test windows-latest py3.11	1m 24s
test windows-latest py3.12	1m 46s
test windows-latest py3.13	1m 41s
	9m 8s