refactor: Rework initial `qOverP` sigma in Examples #22480

Job	Run time
linux_ubuntu	5m 37s
linux_ubuntu_extra (ubuntu2204, 20)	5m 30s
linux_ubuntu_extra (ubuntu2204_clang, 20)	4m 57s
macos	3m 9s
linux_examples_test	11m 29s
linux_physmon	21m 26s
linux_physmon_perf_report	0s
	52m 8s

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