It's possible to (cryptpgraphically verifiably) split up the age verification and the knowledge of what the verification is for.

It would seem like a naive solution would be some arrangement where Discord would ask for a proof-of-age from an official service ran by the State (which issues your ID)

Well you could have government-run cryptographically signed tokens. They're already in the business of holding ID data (i.e. they don't need to collect it and this wouldn't increase the attack surface).

But assuming it has to be a private solution, you could do the same thing but make it a non-profit. Then at least _new_ services you wish to use don't need to collect your ID.