Only switch to Graphene OS if you're willing to use a MitID code display.
I do and honestly don't mind. They're free.
If you insist on the MITID app, just walk away and forget about ditching Google/Apple anytime soon. There is zero indication that anyone with the power to change it gives a shit. I'm not saying it can't change it you pester the right politicians long enough, but the timeframe from you getting an MEP to care to MitID ditching the Google fixation is years if not decades.
But again, you can have full functionality with a little inconvenience by ditching the app.
For banking apps, check the specific ones you need. Nordea works fine, but YMMV.
Mobilepay works as well as it used to for me before switching to Graphene. By that I mean that my experience was regularly getting updates that were buggy as hell (they got better a few years ago, but still among the worst apps for update quality control ime).
Most everything I've tried works just fine - drivers license, Sundhedskort, Min Læge, Digital Post, Aula etc.
BTW, E-boks isn't the official digital mail app anymore. That would be Digital Post.
As for rejsekortet, you can still user a physical card in the future (basis kort) despite the campaigns suggesting the app is mandatory from some time next year.