feat(agent): implement agent execution engine and turn handling with background processing

apps/interfaces/tui/src/view/sidebar.rs

@@ -97,7 +97,13 @@ fn draw_usage_widget(frame: &mut Frame, area: Rect, state: &crate::state::AppSta
         let now_ms = chrono::Utc::now().timestamp_millis();
         let summary = compute_usage_summary(&rt.usage, rt.session_start, now_ms);
         let max_tokens = crate::state::resolve_context_window(&state.app_config, &state.settings);
-        let current_tokens = state.cached_token_count;
+        let current_tokens = if rt.usage.last_tokens_in > 0 {
+            // Actual context window used by the LLM (includes system prompt + tree)
+            rt.usage.last_tokens_in as usize
+        } else {
+            // Fallback for brand new sessions before the first API call
+            state.cached_token_count
+        };
         
         let mut items = vec![
             Line::from(Span::styled(