[diag] Move `otPlatDiagModeGet()` check to `ProcessCmd` #2

Job	Run time
channel-manager-csl	3m 27s
expects	11m 6s
packet-verification-1-1-on-1-4	15m 6s
packet-verification-low-power	10m 4s
thread-1-4-posix	9m 42s
thread-1-4-gcc-m32	11m 48s
thread-1-4-gcc-m64	11m 26s
thread-1-4-clang-m32	9m 59s
thread-1-4-clang-m64	10m 9s
upload-coverage	0s
	1h 32m 47s

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