Does Unstoppable Domains have access to my cryptocurrency funds?

The key point here is your blockchain domain is not a wallet.

When I send funds to yourname.zil the funds are not stored in your blockchain domain.

Your blockchain domain routes cryptocurrency payments.

You connect all your crypto addresses to one domain. Someone who wants to pay you types that domain into a support wallet, the wallet scans the blockchain, finds the correct address, and sends.

The funds are send to the underlying crypto address and the funds are stored there - not inside the blockchain domain.