Hi, Minibits dev here. Ecash privacy model is quite strong with ecash to ecash transactions, as the mint can not differentiate sender nor receiver identity (mint jus blindly swaps ecash tokens provided by receiver for fresh ones).

Cash ins and outs involving lightning transactions share the same privacy model as lightning as such: minibits node sees sender node pubkey and path. Ofc using LBTC swap with LSP like boltz makes your node out of reach, but then the extra privacy gain comes from that swap.