Or, depending on clearances, you could fix the door and fascia piece
together to make a taller door.

Will I be able to get any new integrated dishwasher to fit?
I was thinking of getting MIELE G 5072 SCVi

I would look for drawings to see how they align with your setup, and be
prepared to do some basic carpentry to reuse the door pieces you have.

Theo

Depending on the depth you have, all my kitchen appliances are free
standing behind doors that match my units.