You seem to be making up your own definition of the Layers 😜
But even within your definition, Cashu tokens are a "coupon" or "currency" - because they are a bearer asset, pre-funded by bitcoin (via minting)... which is redeemable on demand by melting back to bitcoin.
In the generally understood definition of Bitcoin layers, Cashu is a Layer 2, because it is a protocol built on top of L1 core to improve scalability, transaction speed, and functionality without altering the L1 code.
The fact it integrates with Lightning doesn't change that, the same way that Liquid integration with Lightning doesn't make it L3 either.
A Cashu mint COULD conceivably mint and melt directly to the L1 chain. It doesn't currently for speed of settlement, but it could. NUT-04/05 are flexible in that regard.
L3 doesn't really exist for Bitcoin - it is the "application layer" - for DApps like you'd find in ETH or SOL.
