This trustless credit system can be built with Spillman payment channels. Spillman channels never gained much popularity because they have two significant drawbacks, they are unidirectional and they expire in a predetermined amount of time. However it just so happens that for this specific use case, those two drawbacks do not matter. Since for this use case the user primarily spends rather than receives money, one way channels work well. The user also already needs to make monthly topup transactions to the mint, so replacing that with a channel that expires every month is no worse.
Without the downsides being an issue, Spillman channels have the benefit that they are very simple. For the user there is no node that needs to be run, no liveness requirement, no complex backup state, no liquidity management. The user only needs to deposit funds into the channel, and simply then sends presigned transactions to the mint offchain to pay over the channel.
In this protocol we propose a novel variant of Spillman channels making use of modern additions to Bitcoin for improved privacy and efficiency. We implement Spillman channels in a way that every possible spending condition can be satisfied by a MuSig2 taproot key path spend. The downside is that interactivity is required for payment, however since interactivity with the mint is already required for issuing ecash tokens, that doesn't add significant complexity.