Electronic – can I repair part fried socket

Assuming your power supply will have the microcontroller to control the power, there are several ways to do this:

• Always have a small voltage and monitor the current. When there's current, there's something connected.

• Have a couple extra pins with a resistor or a diode on it, and use those pins to electrically control the power supply (note: this doesn't even require a microcontroller)

• Have a physical switch in the socket to detect if something is in it

As with literally everything engineering related, be creative. When there's something you want to detect, always ask yourself what its effects will be. Is there a physical state you can measure (with a switch, or a magnetic breaking switch)? Is there an electrical state you can measure (resistance, or an closed circuit)? Then see how you can detect those and use them.

EDIT after your update:

Put a switch on the plug and turn it on when you need it.

This is KN-4A socket. Widely used in Eastern bloc countries in many types of electric equipment with a motor, mostly in sewing machines.

What is important - this socket is not provided for powering up motor or a whole device directly from mains. To make a full circuit you need a steering pedal and special cord. Pedal and cord looks like this (note similar plug but with two contacts):

Pedal controls the speed of the motor, inside of pedal there are switch, capacitor and potentiometer. Or sometimes a rheostat. Or sometimes even a couple of switches and resistors - the more You push the pedal, more resistors are just shorted and motor speed increase. Pedal is connected in series with one of the motor windings. Motor is single phase induction type.

Buying sockets and cords is not a problem, they're still in production because many people still use these (not so) old but very good sewing machines. The best solution - find the original pedal. Or find the parameters of original pedal and choose a similar sewing machine pedal.

If You omit the pedal the motor will be running constantly at full speed. Firstly, it doesn't like it. Secondly - sound from Your harmonica will be awful ;)