refactor: Rework initial `qOverP` sigma in Examples #22460

Job	Run time
macos	3m 20s
linux_ubuntu_extra (ubuntu2204, 20)	5m 23s
linux_ubuntu	5m 23s
linux_ubuntu_extra (ubuntu2204_clang, 20)	5m 9s
linux_physmon	22m 8s
linux_examples_test	6m 33s
linux_physmon_perf_report	0s
	47m 56s

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