> What mechanisms would be in place to allow me to transfer money from my KYC bank account to an anonymous wallet without it being tracked?

I really doubt that they intend do use it, but zero-knowledge cryptography indeed can accomplish this, so there is no technical limitation afaik.

> If the max is €3000 but it's entirely private, how could they possibly know I don't have a higher balance or multiple wallets?

This gets trickier. Let's say we limit to 3000 per account (and use whatever else to limit accounts/person). This would be possible, but would also reveal the amount on the account: try to send decreasing amounts, first one that succeeds reveals previous balance. There's probably an entity that can simulate sending too.

> What tech is even being used to allow fully private, offline transactions in the first place? How does the receiver verify that the digital cash is legit? And how does the network ensure that the money wasn't double spent while offline?

Yeah, this one is impossible.