debugger: Extract running state from DebugSession mode and remove mode field (#29646)

DebugSession.mode is no longer needed because project::debugger::Session
manages its own state now (booting, running, terminated), and removing
mode simplifies a lot of the code that uses running state.

I used Zed AI to do a good chunk of the refactor, but I doubled-checked
everything it did and changed a good amount of its updates.

Release Notes:

- N/A

Co-authored-by: Zed AI <ai@zed.dev>

crates/debugger_ui/src/tests/module_list.rs

@@ -106,10 +106,7 @@ async fn test_module_list(executor: BackgroundExecutor, cx: &mut TestAppContext)
     let running_state =
         active_debug_session_panel(workspace, cx).update_in(cx, |item, window, cx| {
             cx.focus_self(window);
-            item.mode()
-                .as_running()
-                .expect("Session should be running by this point")
-                .clone()
+            item.running_state().clone()
         });
 
     running_state.update_in(cx, |this, window, cx| {