chore: improve serialization of ServerNotification (#3193)

This PR introduces introduces a new
`OutgoingMessage::AppServerNotification` variant that is designed to
wrap a `ServerNotification`, which makes the serialization more
straightforward compared to
`OutgoingMessage::Notification(OutgoingNotification)`. We still use the
latter for serializing an `Event` as a `JSONRPCMessage::Notification`,
but I will try to get away from that in the near future.

With this change, now the generated TypeScript type for
`ServerNotification` is:

```typescript
export type ServerNotification =
  | { "method": "authStatusChange", "params": AuthStatusChangeNotification }
  | { "method": "loginChatGptComplete", "params": LoginChatGptCompleteNotification };
```

whereas before it was:

```typescript
export type ServerNotification =
  | { type: "auth_status_change"; data: AuthStatusChangeNotification }
  | { type: "login_chat_gpt_complete"; data: LoginChatGptCompleteNotification };
```

Once the `Event`s are migrated to the `ServerNotification` enum in Rust,
it should be considerably easier to work with notifications on the
TypeScript side, as it will be possible to `switch (message.method)` and
check for exhaustiveness.

Though we will probably need to introduce:

```typescript
export type ServerMessage = ServerRequest | ServerNotification;
```

and then we still need to group all of the `ServerResponse` types
together, as well.

codex-rs/protocol/src/mcp_protocol.rs

@@ -551,8 +551,8 @@ pub struct AuthStatusChangeNotification {
 }
 
 #[derive(Serialize, Deserialize, Debug, Clone, PartialEq, TS, Display)]
-#[serde(tag = "type", content = "data", rename_all = "snake_case")]
-#[strum(serialize_all = "snake_case")]
+#[serde(tag = "method", content = "params", rename_all = "camelCase")]
+#[strum(serialize_all = "camelCase")]
 pub enum ServerNotification {
     /// Authentication status changed
     AuthStatusChange(AuthStatusChangeNotification),
@@ -561,6 +561,15 @@ pub enum ServerNotification {
     LoginChatGptComplete(LoginChatGptCompleteNotification),
 }
 
+impl ServerNotification {
+    pub fn to_params(self) -> Result<serde_json::Value, serde_json::Error> {
+        match self {
+            ServerNotification::AuthStatusChange(params) => serde_json::to_value(params),
+            ServerNotification::LoginChatGptComplete(params) => serde_json::to_value(params),
+        }
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;