Run template tests

Add `uv` and `pixi`. #1709

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Run time

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Job	Run time
test macos-latest py3.11	17s
test macos-latest py3.12	20s
test macos-latest py3.13	19s
test ubuntu-latest py3.11	34s
test ubuntu-latest py3.12	26s
test ubuntu-latest py3.13	33s
test windows-latest py3.11	49s
test windows-latest py3.12	1m 8s
test windows-latest py3.13	1m 25s
	5m 51s