Another bet could be to let the owner of the identifier (your phone provider, in the instance of a phone number) track what service that identifier points to - like ENUM DNS. But that falls foul of political problems (and risks becoming centralised too).
Federated/decentralised identity is a problem we're actively working on at Matrix, and the DMA will only act to speed up the process, as it's indeed an important piece for this to work well in practice.
Is there a good place to follow this?
Decentralized identities are messy. They only work in cryptobros' dreams. You can't rely on an average person to store a private key. In real life, account recovery is a hard requirement for an identity system, as is the ability to revoke access for someone who has broken into an account.
I may have misread your intent, but honestly I don't see how "user directory" and "privacy" interoperate. What matrix does is maybe prove that you're talking to someone who has access to the same hardware, if not the same person, when you message the same user.
I don't shill for matrix, but I also try to use mastodon to have regular human conversations and I couldn't tell you what service everyone is on...