Run template tests

Add `uv` and `pixi`. #1708

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Run time

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Job	Run time
test macos-latest py3.11	18s
test macos-latest py3.12	19s
test macos-latest py3.13	19s
test ubuntu-latest py3.11	19s
test ubuntu-latest py3.12	27s
test ubuntu-latest py3.13	28s
test windows-latest py3.11	1m 29s
test windows-latest py3.12	1m 24s
test windows-latest py3.13	1m 58s
	7m 1s