TLS already has client side authentication baked in, it's just that no one really uses it or even knows it exists. Most (all?) browsers support it.
https://aboutssl.org/ssl-tls-client-authentication-how-does-...
https://aboutssl.org/ssl-tls-client-authentication-how-does-...
I do use TLS client certificates (with several APIs) but I don't consider them as password replacements (which is the goal of ed25519-login).