Switches and functions of microwave oven unresponsive on cold start
Why does the electronics and the circuits inside the appliance need
such a warm-up before it can operate properly ?

There could be many reasons but I'd put a small wager on it being a leaky electrolytic capacitor. I've had the same problem myself and I found the information on the web about replacing the well-known suspect device and fixed my quite expensive powered speakers.
They just wouldn't activate for about half an hour - it was the anti-pop circuit that was at fault - once the speakers warmed up, it worked fine. I could even turn them off for about a minute and I was able to reactivate them straight away.
Anyway, I'm off on a tangent now so, the message is, it's likely that the problem is a leaky electrolytic capacitor. Search the web for other instances of this happening and see if some folk managed to fix the problem - that's my advice.