refactor: Rework initial `qOverP` sigma in Examples #22456

Job	Run time
linux_ubuntu	5m 21s
linux_ubuntu_extra (ubuntu2204, 20)	6m 27s
macos	4m 16s
linux_ubuntu_extra (ubuntu2204_clang, 20)	5m 3s
linux_examples_test	10m 28s
linux_physmon	12m 24s
linux_physmon_perf_report	1s
	44m 0s

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