Does the coupon code actually redeem Cashu ecash at the mint, or is it just a database lookup linked to a discount?

I have seen your message, will reply later.

No. They're a different type of IOUs, not backed by sats, but by fiat! Paid in cash or card directly to the merchant, and therefore, it's not redeemable at the mint, but in the shop (or online shop) who issued them, for goods or services. No db lookup, just cryptographic validation, then the token get "marked" and removed from the wallet, to prevent double spending. Your question is important. Hope the answer makes sense.