Run template tests

Add FawltyDeps, `deptry` and `pip-check-reqs` as 🟡 good tools. #2308

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Run time

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Job	Run time
test ubuntu-latest py3.13	42s
test ubuntu-latest py3.12	43s
test windows-latest py3.11	1m 21s
test macos-latest py3.11	50s
test ubuntu-latest py3.11	38s
test windows-latest py3.13	1m 41s
test windows-latest py3.12	1m 36s
test macos-latest py3.12	23s
test macos-latest py3.13	36s
	8m 30s