I know this has been asked a few times, but I can't seem to find any updates.
Is there any app or way to add a % surcharge to the final invoice price dependant on the payment method the customer chooses?
If Shopify doesn't offer this an app developer would make a fortune if they could come up with it.
As a workaround, look into this app:
You would be able to add an extra fee on top of the order in general, not necessarily specific to the payment type.