fix: remove mcp-types from app server protocol (#4537)

We continue the separation between `codex app-server` and `codex
mcp-server`.

In particular, we introduce a new crate, `codex-app-server-protocol`,
and migrate `codex-rs/protocol/src/mcp_protocol.rs` into it, renaming it
`codex-rs/app-server-protocol/src/protocol.rs`.

Because `ConversationId` was defined in `mcp_protocol.rs`, we move it
into its own file, `codex-rs/protocol/src/conversation_id.rs`, and
because it is referenced in a ton of places, we have to touch a lot of
files as part of this PR.

We also decide to get away from proper JSON-RPC 2.0 semantics, so we
also introduce `codex-rs/app-server-protocol/src/jsonrpc_lite.rs`, which
is basically the same `JSONRPCMessage` type defined in `mcp-types`
except with all of the `"jsonrpc": "2.0"` removed.

Getting rid of `"jsonrpc": "2.0"` makes our serialization logic
considerably simpler, as we can lean heavier on serde to serialize
directly into the wire format that we use now.

codex-rs/cli/src/login.rs

@@ -1,3 +1,4 @@
+use codex_app_server_protocol::AuthMode;
 use codex_common::CliConfigOverrides;
 use codex_core::CodexAuth;
 use codex_core::auth::CLIENT_ID;
@@ -8,7 +9,6 @@ use codex_core::config::ConfigOverrides;
 use codex_login::ServerOptions;
 use codex_login::run_device_code_login;
 use codex_login::run_login_server;
-use codex_protocol::mcp_protocol::AuthMode;
 use std::path::PathBuf;
 
 pub async fn login_with_chatgpt(codex_home: PathBuf) -> std::io::Result<()> {

codex-rs/cli/src/main.rs

@@ -455,7 +455,7 @@ fn print_completion(cmd: CompletionCommand) {
 mod tests {
     use super::*;
     use codex_core::protocol::TokenUsage;
-    use codex_protocol::mcp_protocol::ConversationId;
+    use codex_protocol::ConversationId;
 
     fn finalize_from_args(args: &[&str]) -> TuiCli {
         let cli = MultitoolCli::try_parse_from(args).expect("parse");