What if the cheater is just running stockfish on a separate laptop, is the anti-cheat system also going to turn on the webcam and track eye movement?

> Being awarded a win by e-mail a day

That is only half of the story. The other half would be in banning the cheater and making them lose access to their account, i.e, impute a real monetary cost to being caught cheating. Make it expensive for those caught cheating and equally expensive for those making false reports and I'd venture that we would see some sort of equilibrium where cheating is not worth it.