Yes, that is the core objective of eIDAS 2.0: proof from the wallet must also be accepted by private sectors (banks, energy, etc.) throughout the EU in future
.
Legally, documents from Austria or Germany are therefore valid everywhere.
However, the truth is that it is still technically unclear whether the interoperability
will function smoothly and comprehensively
from the first wallet generation onwards. In practice, this seamless collaboration will probably
only become established gradually over the course of several updates.