[inquisitor]

I would rather assume an issue with your bank's SMS routing. These bulk SMS service providers which banks and other online services use for SMS delivery often fail to deliver SMS to full MVNOs (such as Lycamobile/toggle) as they either don't have a working route to the corresponding network or because of failing number lookups on the porting database which reveals to which network each single number belongs. It would be interesting to see if German Lycamobile subscribers can receive SMS from your bank which would allow to isolate Lycamobile Germany or toggle as point of failure. But that's obviously impossible from your bank account.
In any case you should complain again with your bank and tell them that you strongly suspect an issue with their SMS provider when delivering SMS to Lycamobile Germany, which is a full MVNO and so requires individual interconnection.