refs #14599 - moved `ShowTime` logic out of timer-related code (#8493) #19607

Job	Run time
build_cmake (ubuntu:25.10, true, true)	5m 49s
build_make (ubuntu:25.10)	4m 48s
build_make (ubuntu:24.04)	4m 23s
build_cmake (alpine:3.23, false, false)	4m 29s
build_make (alpine:3.23)	5m 59s
build_cmake (ubuntu:24.04, true, true)	5m 8s
	30m 36s

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