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/app-server-protocol/src/jsonrpc_lite.rs

@@ -0,0 +1,66 @@
+//! We do not do true JSON-RPC 2.0, as we neither send nor expect the
+//! "jsonrpc": "2.0" field.
+
+use serde::Deserialize;
+use serde::Serialize;
+use ts_rs::TS;
+
+pub const JSONRPC_VERSION: &str = "2.0";
+
+#[derive(Debug, Clone, PartialEq, Deserialize, Serialize, Hash, Eq, TS)]
+#[serde(untagged)]
+pub enum RequestId {
+    String(String),
+    Integer(i64),
+}
+
+pub type Result = serde_json::Value;
+
+/// Refers to any valid JSON-RPC object that can be decoded off the wire, or encoded to be sent.
+#[derive(Debug, Clone, PartialEq, Deserialize, Serialize, TS)]
+#[serde(untagged)]
+pub enum JSONRPCMessage {
+    Request(JSONRPCRequest),
+    Notification(JSONRPCNotification),
+    Response(JSONRPCResponse),
+    Error(JSONRPCError),
+}
+
+/// A request that expects a response.
+#[derive(Debug, Clone, PartialEq, Deserialize, Serialize, TS)]
+pub struct JSONRPCRequest {
+    pub id: RequestId,
+    pub method: String,
+    #[serde(default, skip_serializing_if = "Option::is_none")]
+    pub params: Option<serde_json::Value>,
+}
+
+/// A notification which does not expect a response.
+#[derive(Debug, Clone, PartialEq, Deserialize, Serialize, TS)]
+pub struct JSONRPCNotification {
+    pub method: String,
+    #[serde(default, skip_serializing_if = "Option::is_none")]
+    pub params: Option<serde_json::Value>,
+}
+
+/// A successful (non-error) response to a request.
+#[derive(Debug, Clone, PartialEq, Deserialize, Serialize, TS)]
+pub struct JSONRPCResponse {
+    pub id: RequestId,
+    pub result: Result,
+}
+
+/// A response to a request that indicates an error occurred.
+#[derive(Debug, Clone, PartialEq, Deserialize, Serialize, TS)]
+pub struct JSONRPCError {
+    pub error: JSONRPCErrorError,
+    pub id: RequestId,
+}
+
+#[derive(Debug, Clone, PartialEq, Deserialize, Serialize, TS)]
+pub struct JSONRPCErrorError {
+    pub code: i64,
+    #[serde(default, skip_serializing_if = "Option::is_none")]
+    pub data: Option<serde_json::Value>,
+    pub message: String,
+}