The outgoing EUR wire transfer from my bank fails before or during signing in my online banking

The issue here is on your bank side (nothing to do with Fastpost or OASIS). There are typically three main reasons for this:

1. Some banks infrastructure does not allow their account holders to send instant transactions outside of certain business hours (could be restricted to 8am - 8pm for example). Try again during regular bank business hours.
2. Some banks perform batch jobs for regular outgoing wires that accumulated during the day. Such batch job processing can temporarily prohibit SEPA instant outgoing transactions. Try again later.
3. Some banks may have SEPA instant recipient lists that wrongly identify the TEN31 Bank account with DZ Bank as not SEPA instant capable.

In all cases call your bank and ask them to catch up to the modern times!