Indeed. On-chain is, I think, being discussed here:
I guess that the Cashu proposal assumes that the transaction will be signed and immediately broadcast for confirmation. But I suppose it's shouldn't be too hard to send the signed-but-not-broadcasted vTXO to the ASP instead. Although maybe it's more complex and might require the ASP's involvement (and signature) too
GitHub
onchain bitcoin payment method by gudnuf · Pull Request #283 · cashubtc/nuts
CDK onchain cdk#995
Nutshell
cashu-ts implement onchain (NUT-26) cashu-ts#349
nutmix
