I have the same problem. The support confirms running a custom ROM breaks compatibility. Their advice is to factory reset the phone or use another phone.
The severity of the bug has increased because the SwissID is now mandatory for many governmental services such as the Electronic Patient File.
They are so incompetent because as a fallback you have to use SMS OTP which is not phishing resistant. You cannot switch off SMS OTP.
Is there any collaboration between Graphene and the developers of those root-detecting SDKs? To me it looks like this is a malfunction of an SDK since the phone is not rooted.