I believe you want the order item check here to be invoiceable || has already been invoiced.

If we've previously generated an invoice for some of the order items, those will no longer be invoiceable but shouldn't cause the pop-up if the remaining items are invoiceable

you are correct, I made some changes that should reflect this behavior.
I decided to check invoicebale against encumbered items which should make sense, right?

Additionally added a simple unit test to reinforce this method

clever overriding the toString() here!

Any particular reason to not do it in one loop with something like:
return !orderItems.any{ it -> it.encumbered && !it.invoiceable }

the example you have provided fails on cases where none of our items is encumbered.
If none of them are encumbered it returns false for .any{} and a negation returns true for isFullyInvoiceable which does not make sense which is why I added an additional check for if there are any encumbered items.

Last thought: What about adjustments? If we have items that are encumbered and non-invoiceable, but we have an invoiceable adjustment, we'd still want the confirmation to pop up, right?

Would not encumberedOrderItems?.every { it -> it.invoiceable } be cleaner? Plus this should also look into orderAdjustments, because if you won't have order items, just order adjustments, then you will always get the warning. On top of that invoiceable checks if item is invoiceable, not fully invoiceable, as you can see, there is
quantityAvailableToInvoice > 0 and in you case you are more interested in if quantityAvailableToInvoice == quantity remaining to invoice

good point on the adjustments but as for return encumberedOrderItems?.every { it -> it.invoiceable } this will not work since it is not the same as return encumberedOrderItems && encumberedOrderItems.every { it -> it.invoiceable }
The first check for encumberedOrderItems is for a case where we do .every on an empty list that will return true and we don't want that