To come back to the example of CashApp:
My definition of “using bitcoin” is when a transaction happens on lightning or on chain. So CashApp-to-CashApp is not using bitcoin since I assume it’s just a database transaction.
However, I would consider CashApp to any other lightning node or vice versa “using bitcoin”, yes, even if the other entity is also a custodial service.
So yes, you can use bitcoin with cashu as long as an actual transaction happens on the network. So mint and melt, but not swaps.