Run template tests

Use `actions/deploy-pages` to deploy docs in template (#578) #2359

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Run time

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Job	Run time
test macos-latest py3.13	33s
test ubuntu-latest py3.13	42s
test ubuntu-latest py3.12	44s
test windows-latest py3.11	1m 51s
test ubuntu-latest py3.11	44s
test macos-latest py3.12	45s
test macos-latest py3.11	32s
test windows-latest py3.13	2m 0s
test windows-latest py3.12	1m 30s
	9m 21s