No one is required to use EUDI: https://ec.europa.eu/digital-building-blocks/sites/spaces/EU...

Companies and providers (like banks) have to support it, but use is voluntary.

Check out the spec and legal framework, it actually makes sense and is open to different implementations, though you might need to certify it.

I wonder if there will be a big enough market for a very compact smartphone equivalent device that can be used just for credentials? A device that is offline on standby except when you need it. Perhaps the size of a car key.

You're screwed. This has been the way for a while now. You cannot exist in society without a smart phone and it's only going to get worse.