[diag] Move `otPlatDiagModeGet()` check to `ProcessCmd` #4

Job	Run time
channel-manager-csl	3m 3s
expects	31m 54s
packet-verification-1-1-on-1-4	11m 33s
packet-verification-low-power	9m 42s
thread-1-4-gcc-m32	11m 49s
thread-1-4-posix	9m 40s
thread-1-4-gcc-m64	11m 49s
thread-1-4-clang-m32	10m 0s
thread-1-4-clang-m64	9m 27s
upload-coverage	0s
	1h 48m 57s

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