When transfer switch will move from shore power to generator with no blink, going back might be a different story.
When shutting down Generator engine will hesitate for a second or 3, what can make transfer switch flapping, or give low voltage before it switch.
Meaning make sure all sensitive appliances and especially AC are off for the moment.
Who told you the need for monthly run?
I just started my Generac first time after at least 4 years. All it took was pushing fuel prime button for 4 seconds and it fire right up.
But I run carburetor dry and drain the tank before.
My portable Honda generator is known to sit for 2 years between uses and never hesitated to start on old fuel. But again, I run carburetor dry before putting it off.