That would be my biggest worry as well. Although this isn't specified yet, I assume that they would develop the software for Google/Apple. IIRC the Digitale Gesellschaft, a privacy advocacy group, has mentioned this as feedback about a year ago. I don't know what was done with that though. Other issues were included in the development plan though.

Also: With how this law is worded, no one is forced to use an eID. You can go the old fashioned way and e.g. go to the traffic office in person.