feat(app-server): update remote control APIs for better UX (#22877)

## Why
To help improve `codex remote-control` CLI UX which I plan to do in a
followup, this PR adds `server-name` to the various remote control APIs:
- `remoteControl/enable`
- `remoteControl/disable`
- `remoteControl/status/changed`

Also, add a `remoteControl/status/read` API. This will be helpful in the
Codex App.

codex-rs/app-server-protocol/src/protocol/common.rs

@@ -812,6 +812,12 @@ client_request_definitions! {
         serialization: global("remote-control"),
         response: v2::RemoteControlDisableResponse,
     },
+    #[experimental("remoteControl/status/read")]
+    RemoteControlStatusRead => "remoteControl/status/read" {
+        params: #[ts(type = "undefined")] #[serde(skip_serializing_if = "Option::is_none")] Option<()>,
+        serialization: global_shared_read("remote-control"),
+        response: v2::RemoteControlStatusReadResponse,
+    },
     #[experimental("collaborationMode/list")]
     /// Lists collaboration mode presets.
     CollaborationModeList => "collaborationMode/list" {

codex-rs/app-server-protocol/src/protocol/v2/remote_control.rs

@@ -9,6 +9,7 @@ use ts_rs::TS;
 #[ts(export_to = "v2/")]
 pub struct RemoteControlStatusChangedNotification {
     pub status: RemoteControlConnectionStatus,
+    pub server_name: String,
     pub installation_id: String,
     pub environment_id: Option<String>,
 }
@@ -18,6 +19,7 @@ pub struct RemoteControlStatusChangedNotification {
 #[ts(export_to = "v2/")]
 pub struct RemoteControlEnableResponse {
     pub status: RemoteControlConnectionStatus,
+    pub server_name: String,
     pub installation_id: String,
     pub environment_id: Option<String>,
 }
@@ -27,6 +29,17 @@ pub struct RemoteControlEnableResponse {
 #[ts(export_to = "v2/")]
 pub struct RemoteControlDisableResponse {
     pub status: RemoteControlConnectionStatus,
+    pub server_name: String,
+    pub installation_id: String,
+    pub environment_id: Option<String>,
+}
+
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, Eq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct RemoteControlStatusReadResponse {
+    pub status: RemoteControlConnectionStatus,
+    pub server_name: String,
     pub installation_id: String,
     pub environment_id: Option<String>,
 }
@@ -45,11 +58,13 @@ impl From<RemoteControlStatusChangedNotification> for RemoteControlEnableRespons
     fn from(notification: RemoteControlStatusChangedNotification) -> Self {
         let RemoteControlStatusChangedNotification {
             status,
+            server_name,
             installation_id,
             environment_id,
         } = notification;
         Self {
             status,
+            server_name,
             installation_id,
             environment_id,
         }
@@ -60,11 +75,13 @@ impl From<RemoteControlStatusChangedNotification> for RemoteControlDisableRespon
     fn from(notification: RemoteControlStatusChangedNotification) -> Self {
         let RemoteControlStatusChangedNotification {
             status,
+            server_name,
             installation_id,
             environment_id,
         } = notification;
         Self {
             status,
+            server_name,
             installation_id,
             environment_id,
         }