[connectors] Support connectors part 1 - App server & MCP (#9667)

In order to make Codex work with connectors, we add a built-in gateway
MCP that acts as a transparent proxy between the client and the
connectors. The gateway MCP collects actions that are accessible to the
user and sends them down to the user, when a connector action is chosen
to be called, the client invokes the action through the gateway MCP as
well.

 - [x] Add the system built-in gateway MCP to list and run connectors.
 - [x] Add the app server methods and protocol

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

@@ -965,6 +965,39 @@ pub struct ListMcpServerStatusResponse {
     pub next_cursor: Option<String>,
 }
 
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, Default, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct AppsListParams {
+    /// Opaque pagination cursor returned by a previous call.
+    pub cursor: Option<String>,
+    /// Optional page size; defaults to a reasonable server-side value.
+    pub limit: Option<u32>,
+}
+
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct AppInfo {
+    pub id: String,
+    pub name: String,
+    pub description: Option<String>,
+    pub logo_url: Option<String>,
+    pub install_url: Option<String>,
+    #[serde(default)]
+    pub is_accessible: bool,
+}
+
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct AppsListResponse {
+    pub data: Vec<AppInfo>,
+    /// Opaque cursor to pass to the next call to continue after the last item.
+    /// If None, there are no more items to return.
+    pub next_cursor: Option<String>,
+}
+
 #[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
 #[serde(rename_all = "camelCase")]
 #[ts(export_to = "v2/")]