Run template tests

Add `uv` and `pixi`. #1710

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Run time

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Job	Run time
test macos-latest py3.11	23s
test macos-latest py3.12	24s
test macos-latest py3.13	18s
test ubuntu-latest py3.11	21s
test ubuntu-latest py3.12	22s
test ubuntu-latest py3.13	36s
test windows-latest py3.11	1m 1s
test windows-latest py3.12	1m 18s
test windows-latest py3.13	1m 33s
	6m 16s