there could be a way to implement a client-side PoW integrated with the cryptographic process of the swap? Maybe with a difficulty controlled arbitrarly by mint itself. In the end theres a lot of trust in mint to not rug and to keep their services online, adding a pow requirement to raise on necessity (or raise slowly with years as computing powers for users increase) dont change nothing in that sense.

Keep the pow requirement something like that a current gen smartphone can solve in 1-2 seconds could be enough.