Run template tests

Use `actions/deploy-pages` to deploy docs in template #2350

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Run time

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Job	Run time
test macos-latest py3.13	34s
test windows-latest py3.11	1m 45s
test ubuntu-latest py3.12	41s
test windows-latest py3.12	2m 4s
test macos-latest py3.11	32s
test macos-latest py3.12	46s
test ubuntu-latest py3.13	45s
test ubuntu-latest py3.11	51s
test windows-latest py3.13	1m 56s
	9m 54s