A bit of a stretch to call 'don’t set off nukes on the say-so of Trump’ a “coup.” Usually that term implies a positive acquisition of power, not a temporary pause or set of oversight-provisions on the power of another. (It’s debatable, I’ll grant.)
Yes, it does appear that Milley did NOT have Constitutional authority for saying ‘don’t let Trump push the button unless there’s confirmation’.
And yes, it’s clear that such eventualities need more codification.
But it’s also clear that no level of mental illness in that President was going to result in the 25th Amendment being deployed. At this point we might as well have a new amendment rescinding the 25th–no one will ever have the courage to use it, if they didn’t have the courage to use it in this situation.
So provisions for this kind of eventuality need to be made. “Presidents can do whatever they wish with our nuclear arsenal no matter how demonstrably irresponsible and destructive” does NOT seem to be a viable policy, going forward.