MKS DLC32 Board Disconnects Caused by Auto Air Assist

I’d try swapping the relay out for an solid state relay eliminating the mechanical relay.
In all prabability, the supply line has a transient or interference generated by the switching of the compressor.
Ensure there is plenty of power for all of these devices to use. Isolating the compressor from the supply lines of the controller or pc might be an easy test…
When you switch a mechanical relay on, it switches, without regard to the switched voltage. If you switch it on at 120V it will draw a surge of current, it can also arc when it turns off.
A ssr will switch at zero voltage, both on and off. And it will also last a lifetime.