To be clear; the Nintendo Switch tends to trade fluently in cryptographic certificates.
The MiG Switch has one of these certificates; one it’s creators likely copied from a legitimate Nintendo Switch game title. All games have such certificates and they are uniquely serialized; much like a GUID or UUID would be. These certificates are signed by the Game Dev studio, and then Nintendo in a typical certificate signing chain scheme; Nintendo signs the Game Dev Studio cert, which signs the Title certificate, which signs the unique cart or digital copy cert.
This banning is usually achieved by banning either the lowest certificate in the chain or the one directly above it; or even the Dev Cert if it was compromised.
So the MiG Switch carts are likely hardware banned. Your Nintendo Switch probably advertises to Nintendo which cart(s) were inserted into it recently by sharing the fingerprints of the certificates. Then Nintendo can basically kill the certificate assigned to your Switch system and prevent you from connecting online; as your Switch uses it’s own system cert to identify itself to Nintendo services.
In all cases this is un-evade-able when connecting to the internet; as Nintendo Switch system certs are burned into a PROM chip on the main board at manufacture. This chip is a WORM chip, which can only be written once and read many billions of times.
A critical part of the way they try and curb cheating in online play is checking the integrity of the runtime environment; which includes checking what titles were launched recently; and if that happens to include a certificate they’ve banned for being cloned by the MiG Switch; then you’ll quickly be banned by their anti-cheating hammer.
Most important is those checks typically don’t take place naturally; they only occur when you’re connecting to the EShop, or connecting to NN to play multiplayer online. The devil therein unfortunately lies in the details; and if you’ve ever purchased a Digital Title that means your Switch is regularly connecting to the EShop to renew Digital License Tickets needed. They tend to expire every 72 hours and must be renewed by presenting an expired Ticket, a valid Ticket Granting Ticket (given to your Switch when you buy the title) and contacting “Mommy Nintendo” and asking “Mommy, May I?”. Yeah. DRM sucks.
If all goes well; your Switch gets a shiny new set of tickets. Unfortunately Nintendo was paying attention to requests and will issue out regular waves of bans for systems detected cheating. You won’t know when this will happen, and it won’t prevent Nintendo from letting you play your games; you’ll just suddenly find your Switch banned from online play after such ban waves.