Add app-server background terminal process APIs (#26041)

## Summary

Codex Apps needs app-server as the source of truth for chat-started
background terminals instead of guessing from local process trees.

This PR adds experimental v2 APIs to list and terminate background
terminals for a loaded thread using app-server process ids, so clients
can manage background terminals without local PID discovery.

## Changes

- `thread/backgroundTerminals/list` returns paginated background
terminal records with `itemId`, app-server `processId`, `command`,
`cwd`, nullable `osPid`, nullable `cpuPercent`, and nullable `rssKb`.
- `thread/backgroundTerminals/terminate` terminates one running
background terminal by app-server `processId` and returns whether a
process was terminated.
- Background terminal list and terminate operations use unified-exec
process manager state as their source of truth.

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

@@ -935,6 +935,57 @@ pub struct ThreadBackgroundTerminalsCleanParams {
 #[ts(export_to = "v2/")]
 pub struct ThreadBackgroundTerminalsCleanResponse {}
 
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct ThreadBackgroundTerminalsListParams {
+    pub thread_id: String,
+    /// Opaque pagination cursor returned by a previous call.
+    #[ts(optional = nullable)]
+    pub cursor: Option<String>,
+    /// Optional page size.
+    #[ts(optional = nullable)]
+    pub limit: Option<u32>,
+}
+
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct ThreadBackgroundTerminal {
+    pub item_id: String,
+    pub process_id: String,
+    pub command: String,
+    pub cwd: AbsolutePathBuf,
+    pub os_pid: Option<u32>,
+    pub cpu_percent: Option<f64>,
+    pub rss_kb: Option<u64>,
+}
+
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct ThreadBackgroundTerminalsListResponse {
+    pub data: Vec<ThreadBackgroundTerminal>,
+    /// 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/")]
+pub struct ThreadBackgroundTerminalsTerminateParams {
+    pub thread_id: String,
+    pub process_id: String,
+}
+
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct ThreadBackgroundTerminalsTerminateResponse {
+    pub terminated: bool,
+}
+
 #[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
 #[serde(rename_all = "camelCase")]
 #[ts(export_to = "v2/")]