There's two ways to make extensions to Zed, providing context for AI. In the post they show off making a Rust -> WASM based extension and also mention a server based model. There's also a third option -- Zed is open source. You don't have to use their auth, it just makes collaboration easy.
we call the latter a "Context Server", basically any process that communicates via JSON-RPC over stdio can do it. documentation for that is here: https://zed.dev/docs/assistant/context-servers