Hi Sven, the ECU in my car was replaced once long before I owned it and there has been other issues with various later models I understand.
It is probably the most technical part of the car and requires expert repair or replacement if it fails. It is also early technology which possibly does not help its reliability.
In my experience it is best to check or replace the easier/ cheaper parts first if only to eliminate them.
Try these things first and check one at a time. (Based on my personal experience)
Reset the ECU by turning off and on the red switch behind your seat, (presume you have a red switch?)
( don’t start with your foot on the accelerator as this will over fuel).
Check the seating/ or swap fuel pump relay.
Clean fuel pump connections.
Replace the fuel filter.
Regards John k