If the new binary is literally identical to the last one which was passed validation, absolutely zero additional testing is required. It is a waste of resources to retest an identical binary (assuming everything else can be held constant of course, which obviously can't always be the case).
Actually sending our hypothetical refactoring to production would itself be a waste of resources anyway, since the binary is identical... you just skip it, wait for the next real change, and then proceed as usual.
All processes have exceptions, the "binary identical output" is an easy one if your leadership chain is capable of understanding it.
And to be clear, "binary" here could absolutely mean "entire firmware image". The era of reproducible builds is upon us, and it is glorious.