MitID is different from the proposed app-based solution for age verification which is designed to not leave a trail. The age verification app will initially be enrolled using MitID (or perhaps by a physical visit to a citizen service point where you can show physical credentials and answer security questions), but subsequent presentations of age verification proofs to service providers will be done without involving a central party.
All in all it is a good design from a privacy perspective. The major issue with it is that ONLY a smartphone based solution is planned, and that there is a high likelihood that it will depend on Play Integrity attestation. This will force everyone to be customers of Google or Apple if they want access to the full internet. I think it is technically possible to also offer alternative solutions based on secure hardware tokens which would still enable people without smartphones to verify their age in a privacy preserving way, but this is not planned.