Refactor param handling of `pset.execute` #1346

Job	Run time
py3.12 \| ubuntu \| unit tests	4m 16s
py3.11 \| ubuntu \| unit tests	3m 58s
mypy	0s
py${{ matrix.python-version }} \| ${{ matrix.os }} \| integration tests	0s
merge-test-artifacts	0s
	8m 14s

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