Run template tests

Use `actions/deploy-pages` to deploy docs in template #2351

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Run time

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Job	Run time
test windows-latest py3.13	1m 49s
test macos-latest py3.13	43s
test ubuntu-latest py3.11	44s
test ubuntu-latest py3.12	42s
test windows-latest py3.11	1m 40s
test ubuntu-latest py3.13	47s
test macos-latest py3.12	39s
test macos-latest py3.11	40s
test windows-latest py3.12	1m 34s
	9m 18s