fix: separate codex mcp into codex mcp-server and codex app-server (#4471)

This is a very large PR with some non-backwards-compatible changes.

Historically, `codex mcp` (or `codex mcp serve`) started a JSON-RPC-ish
server that had two overlapping responsibilities:

- Running an MCP server, providing some basic tool calls.
- Running the app server used to power experiences such as the VS Code
extension.

This PR aims to separate these into distinct concepts:

- `codex mcp-server` for the MCP server
- `codex app-server` for the "application server"

Note `codex mcp` still exists because it already has its own subcommands
for MCP management (`list`, `add`, etc.)

The MCP logic continues to live in `codex-rs/mcp-server` whereas the
refactored app server logic is in the new `codex-rs/app-server` folder.
Note that most of the existing integration tests in
`codex-rs/mcp-server/tests/suite` were actually for the app server, so
all the tests have been moved with the exception of
`codex-rs/mcp-server/tests/suite/mod.rs`.

Because this is already a large diff, I tried not to change more than I
had to, so `codex-rs/app-server/tests/common/mcp_process.rs` still uses
the name `McpProcess` for now, but I will do some mechanical renamings
to things like `AppServer` in subsequent PRs.

While `mcp-server` and `app-server` share some overlapping functionality
(like reading streams of JSONL and dispatching based on message types)
and some differences (completely different message types), I ended up
doing a bit of copypasta between the two crates, as both have somewhat
similar `message_processor.rs` and `outgoing_message.rs` files for now,
though I expect them to diverge more in the near future.

One material change is that of the initialize handshake for `codex
app-server`, as we no longer use the MCP types for that handshake.
Instead, we update `codex-rs/protocol/src/mcp_protocol.rs` to add an
`Initialize` variant to `ClientRequest`, which takes the `ClientInfo`
object we need to update the `USER_AGENT_SUFFIX` in
`codex-rs/app-server/src/message_processor.rs`.

One other material change is in
`codex-rs/app-server/src/codex_message_processor.rs` where I eliminated
a use of the `send_event_as_notification()` method I am generally trying
to deprecate (because it blindly maps an `EventMsg` into a
`JSONNotification`) in favor of `send_server_notification()`, which
takes a `ServerNotification`, as that is intended to be a custom enum of
all notification types supported by the app server. So to make this
update, I had to introduce a new variant of `ServerNotification`,
`SessionConfigured`, which is a non-backwards compatible change with the
old `codex mcp`, and clients will have to be updated after the next
release that contains this PR. Note that
`codex-rs/app-server/tests/suite/list_resume.rs` also had to be update
to reflect this change.

I introduced `codex-rs/utils/json-to-toml/src/lib.rs` as a small utility
crate to avoid some of the copying between `mcp-server` and
`app-server`.

codex-rs/mcp-server/src/message_processor.rs

@@ -1,14 +1,12 @@
 use std::collections::HashMap;
 use std::path::PathBuf;
 
-use crate::codex_message_processor::CodexMessageProcessor;
 use crate::codex_tool_config::CodexToolCallParam;
 use crate::codex_tool_config::CodexToolCallReplyParam;
 use crate::codex_tool_config::create_tool_for_codex_tool_call_param;
 use crate::codex_tool_config::create_tool_for_codex_tool_call_reply_param;
 use crate::error_code::INVALID_REQUEST_ERROR_CODE;
 use crate::outgoing_message::OutgoingMessageSender;
-use codex_protocol::mcp_protocol::ClientRequest;
 use codex_protocol::mcp_protocol::ConversationId;
 
 use codex_core::AuthManager;
@@ -38,7 +36,6 @@ use tokio::sync::Mutex;
 use tokio::task;
 
 pub(crate) struct MessageProcessor {
-    codex_message_processor: CodexMessageProcessor,
     outgoing: Arc<OutgoingMessageSender>,
     initialized: bool,
     codex_linux_sandbox_exe: Option<PathBuf>,
@@ -56,16 +53,8 @@ impl MessageProcessor {
     ) -> Self {
         let outgoing = Arc::new(outgoing);
         let auth_manager = AuthManager::shared(config.codex_home.clone());
-        let conversation_manager = Arc::new(ConversationManager::new(auth_manager.clone()));
-        let codex_message_processor = CodexMessageProcessor::new(
-            auth_manager,
-            conversation_manager.clone(),
-            outgoing.clone(),
-            codex_linux_sandbox_exe.clone(),
-            config,
-        );
+        let conversation_manager = Arc::new(ConversationManager::new(auth_manager));
         Self {
-            codex_message_processor,
             outgoing,
             initialized: false,
             codex_linux_sandbox_exe,
@@ -75,17 +64,6 @@ impl MessageProcessor {
     }
 
     pub(crate) async fn process_request(&mut self, request: JSONRPCRequest) {
-        if let Ok(request_json) = serde_json::to_value(request.clone())
-            && let Ok(codex_request) = serde_json::from_value::<ClientRequest>(request_json)
-        {
-            // If the request is a Codex request, handle it with the Codex
-            // message processor.
-            self.codex_message_processor
-                .process_request(codex_request)
-                .await;
-            return;
-        }
-
         // Hold on to the ID so we can respond.
         let request_id = request.id.clone();