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.rs

@@ -118,8 +118,8 @@ pub fn start_debug_session_with<T: Fn(&Arc<DebugAdapterClient>) + 'static>(
         workspace
             .panel::<DebugPanel>(cx)
             .and_then(|panel| panel.read(cx).active_session())
-            .and_then(|session| session.read(cx).mode().as_running().cloned())
-            .map(|running| running.read(cx).session().clone())
+            .map(|session| session.read(cx).running_state().read(cx).session())
+            .cloned()
             .ok_or_else(|| anyhow!("Failed to get active session"))
     })??;