Preserve background terminals on interrupt and rename cleanup command to /stop (#14602)

### Motivation
- Interrupting a running turn (Ctrl+C / Esc) currently also terminates
long‑running background shells, which is surprising for workflows like
local dev servers or file watchers.
- The existing cleanup command name was confusing; callers expect an
explicit command to stop background terminals rather than a UI clear
action.
- Make background‑shell termination explicit and surface a clearer
command name while preserving backward compatibility.

### Description
- Renamed the background‑terminal cleanup slash command from `Clean`
(`/clean`) to `Stop` (`/stop`) and kept `clean` as an alias in the
command parsing/visibility layer, updated the user descriptions and
command popup wiring accordingly.
- Updated the unified‑exec footer text and snapshots to point to `/stop`
(and trimmed corresponding snapshot output to match the new label).
- Changed interrupt behavior so `Op::Interrupt` (Ctrl+C / Esc interrupt)
no longer closes or clears tracked unified exec / background terminal
processes in the TUI or core cleanup path; background shells are now
preserved after an interrupt.
- Updated protocol/docs to clarify that `turn/interrupt` (or
`Op::Interrupt`) interrupts the active turn but does not terminate
background terminals, and that `thread/backgroundTerminals/clean` is the
explicit API to stop those shells.
- Updated unit/integration tests and insta snapshots in the TUI and core
unified‑exec suites to reflect the new semantics and command name.

### Testing
- Ran formatting with `just fmt` in `codex-rs` (succeeded). 
- Ran `cargo test -p codex-protocol` (succeeded). 
- Attempted `cargo test -p codex-tui` but the build could not complete
in this environment due to a native build dependency that requires
`libcap` development headers (the `codex-linux-sandbox` vendored build
step); install `libcap-dev` / make `libcap.pc` available in
`PKG_CONFIG_PATH` to run the TUI test suite locally.
- Updated and accepted the affected `insta` snapshots for the TUI
changes so visual diffs reflect the new `/stop` wording and preserved
interrupt behavior.

------
[Codex
Task](https://chatgpt.com/codex/tasks/task_i_69b39c44b6dc8323bd133ae206310fae)

codex-rs/tui/src/chatwidget/tests.rs

@@ -3820,7 +3820,7 @@ async fn enqueueing_history_prompt_multiple_times_is_stable() {
 }
 
 #[tokio::test]
-async fn streaming_final_answer_keeps_task_running_state() {
+async fn streaming_final_answer_ctrl_c_interrupt_preserves_background_shells() {
     let (mut chat, mut rx, mut op_rx) = make_chatwidget_manual(None).await;
     chat.thread_id = Some(ThreadId::new());
 
@@ -3843,12 +3843,16 @@ async fn streaming_final_answer_keeps_task_running_state() {
     );
     assert_matches!(op_rx.try_recv(), Err(TryRecvError::Empty));
 
+    begin_unified_exec_startup(&mut chat, "call-1", "process-1", "npm run dev");
+    assert_eq!(chat.unified_exec_processes.len(), 1);
+
     chat.handle_key_event(KeyEvent::new(KeyCode::Char('c'), KeyModifiers::CONTROL));
     match op_rx.try_recv() {
         Ok(Op::Interrupt) => {}
         other => panic!("expected Op::Interrupt, got {other:?}"),
     }
     assert!(!chat.bottom_pane.quit_shortcut_hint_visible());
+    assert_eq!(chat.unified_exec_processes.len(), 1);
 }
 
 #[tokio::test]
@@ -6025,10 +6029,10 @@ async fn slash_exit_requests_exit() {
 }
 
 #[tokio::test]
-async fn slash_clean_submits_background_terminal_cleanup() {
+async fn slash_stop_submits_background_terminal_cleanup() {
     let (mut chat, mut rx, mut op_rx) = make_chatwidget_manual(None).await;
 
-    chat.dispatch_command(SlashCommand::Clean);
+    chat.dispatch_command(SlashCommand::Stop);
 
     assert_matches!(op_rx.try_recv(), Ok(Op::CleanBackgroundTerminals));
     let cells = drain_insert_history(&mut rx);
@@ -9061,7 +9065,7 @@ async fn interrupt_prepends_queued_messages_before_existing_composer_text() {
 }
 
 #[tokio::test]
-async fn interrupt_clears_unified_exec_processes() {
+async fn interrupt_keeps_unified_exec_processes() {
     let (mut chat, mut rx, _op_rx) = make_chatwidget_manual(None).await;
 
     begin_unified_exec_startup(&mut chat, "call-1", "process-1", "sleep 5");
@@ -9076,7 +9080,7 @@ async fn interrupt_clears_unified_exec_processes() {
         }),
     });
 
-    assert!(chat.unified_exec_processes.is_empty());
+    assert_eq!(chat.unified_exec_processes.len(), 2);
 
     let _ = drain_insert_history(&mut rx);
 }
@@ -9119,7 +9123,7 @@ async fn review_ended_keeps_unified_exec_processes() {
 }
 
 #[tokio::test]
-async fn interrupt_clears_unified_exec_wait_streak_snapshot() {
+async fn interrupt_preserves_unified_exec_wait_streak_snapshot() {
     let (mut chat, mut rx, _op_rx) = make_chatwidget_manual(None).await;
 
     chat.handle_codex_event(Event {
@@ -9150,7 +9154,7 @@ async fn interrupt_clears_unified_exec_wait_streak_snapshot() {
         .collect::<Vec<_>>()
         .join("\n");
     let snapshot = format!("cells={}\n{combined}", cells.len());
-    assert_snapshot!("interrupt_clears_unified_exec_wait_streak", snapshot);
+    assert_snapshot!("interrupt_preserves_unified_exec_wait_streak", snapshot);
 }
 
 #[tokio::test]