It depends on your precise requirements and assumptions.
Does your definition of 'privacy-preserving' distrust Google, Apple, Xiaomi, HTC, Honor, Samsung and suchlike?
Do you also distrust third-party clowns like experian and equifax (whose current systems have gaping security holes) and distrust large government IT projects (which are outsourced to clowns like Fujutsu who don't know what they're doing) ??
Do you require it to work on all devices, including outdated phones and tablets; PCs; Linux-only devices; other networked devices like smart lightbulbs; and so on? Does it have to work in places phones aren't allowed, or mobile data/bluetooth isn't available? Does the identity card have to be as thin, flexible, durable and cheap as a credit card, precluding any built-in fingerprint sensors and suchlike?
Does the age validation have to protect against an 18-year-old passing the age check on their 16-year-old friend's account? While also being privacy-preserving enough nobody can tell the two accounts were approved with the same ID card?
Does the system also have to work on websites without user accounts, because who the hell creates a pornhub account anyway?
Does the system need to work without the government approving individual websites' access to the system? Does it also need to be support proving things like name, nationality, and right to work in the country so people can apply for bank accounts and jobs online? And yet does it need to prevent sites from requiring names just for ad targeting purposes?
Do all approvals have to be provable, so every company can prove to the government that the checks were properly carried out at the right time? Does it have to be possible to revoke cards in a timely manner, but without maintaining a huge list of revoked cards, and without every visit to a porn site triggering a call to a government server for a revocation check?
If you want to accomplish all of these goals - you're going to have a tough time.