There are already online ID verification services for all kinds of apps.
Most of the EU's EIDAS proposal - apart from the "we control your TLS certificates" paragraph - is about building a reliable online identification service that preserves as much privacy as possible. I think one of the ideas is to be able to prove you are (or at least hold the ID card and PIN of) an 18+ EU citizen, without divulging your identity. Part of the bill is then to make it mandatory for businesses that want to do citizenship/age verification to accept this method unless they have a really good reason not to.
Once you've verified someone's ID, if the law doesn't require this then you don't have to save it in any form, so all a hacker would get if they break in to the database later is that the boolean flag is_verified is set on a particular account (along with the usual things such as the password hash and the email address).
For comparison, I'm always a bit uneasy when a site needs my mobile number "to verify you're a human and prevent spam" but they definitely won't save it or use it for marketing purposes - I don't trust everyone. But I would trust a properly designed and audited privacy-preserving ID protocol, just like I trust using the same yubikey across different sites.
However, I certainly don't believe that: I believe that having a giant centralized verification service is inherently dangerous in a world where we are apparently reliant on inanity like CrowdStrike to feel a sense of security; and, in fact, there was even just recently a big hack of an identity provider company.
https://www.eff.org/deeplinks/2024/06/hack-age-verification-...
[0] https://www.mdlconnection.com/implementation-tracker-map/
(Note that I'm not saying this bill requires age verification, nor that it doesn't: I am merely responding to the suggestion to build "verified 18+ networks" as a way of easily being compliant.)