The "app" could be a good solution, if it didn't require attested Android or iOS. It could, for example, have me plug my ID chip into my GNU/Linux system and expose it with a standard protocol. That would be no problem. The problem is that they do not want such a way.
In any case, I think that age gating would not be needed if the platforms were regulated to remove addictive recommendation algorithms.
ID chip? Is that something everybody in the EU (or whatever region) has? Is it just embedded in your driver license or passport?
[I'm in the US, we're very ID-averse here, weird, but is what it is]
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Using an ID card reader is already possible. See here for a list of Linux repos supporting German IDs: https://www.ausweisapp.bund.de/en/open-source Finding a working hardware/software combination for your ID card is up to you.
The app is an alternative for people who don't want to buy or carry around a card reader, but who already have a smartphone.
It is possible for e-signatures and similar variants. However, there is no sign that the "age verification" will support this variant. If you go to the demo <https://cinema.ageverification.dev>, no option is given other than the Android/iOS app.
So it seems that the app is only an alternative in the case of government portals, but it is not an alternative for "age verification".