Latest update from today:
I received my MitID code viewer (the hardware gadget)
I activated it using the MitID app on my old, still working phone (an iPhone)
On a computer I logged into my bank using the now activated code viewer → worked
I installed MobilePay on the FP5, got to the MitID login, entered the code from the code viewer → 
Error: Whoops! Something went wrong. Please try again later.
So I’m assuming it’s the same problem as with MitID: “Device integrity can’t be verified, therefore we won’t let you use this app on this phone.”
Side note (let’s not widen the scope of this thread too much, but thought it was relevant to the topic): As I went on with setting up other things on the phone I tried installing Authy (the MFA app on my iPhone) and that was blocked, too… After some reading and some more: I’m switching to Aegis.
So I think I won’t to tinker much more now as I don’t want to apply too many “hacks” to the /e/OS operating system, so that my hacky fixes don’t accidentally interfere with the otherwise perfectly functional system.
I’ll wait patiently and hope for a “proper” fix by microG or /e/OS 
If anyone finds solutions, or has ideas for fixes, please do share them as they might still help other people (and even convince me to try more hacky things anyway).
I will of course update this post, should I happen to stumble upon a fix.