Refactor to use new ACP crate (#35043)

This will prepare us for running the protocol over MCP

Release Notes:

- N/A

---------

Co-authored-by: Ben Brandt <benjamin.j.brandt@gmail.com>
Co-authored-by: Conrad Irwin <conrad.irwin@gmail.com>
Co-authored-by: Richard Feldman <oss@rtfeldman.com>

crates/agent_servers/Cargo.toml

@@ -18,6 +18,7 @@ doctest = false
 
 [dependencies]
 acp_thread.workspace = true
+agent-client-protocol.workspace = true
 agentic-coding-protocol.workspace = true
 anyhow.workspace = true
 collections.workspace = true