agent ctx-badge: seed Bus::last_usage from latest turn_stats row on startup

hive-ag3nt/src/events.rs

@@ -378,6 +378,15 @@ impl Bus {
         self.emit(LiveEvent::ModelChanged { model: value });
     }
 
+    /// Seed `last_usage` at startup without emitting a SSE event.
+    /// Used by the bin entrypoints to backfill from the most recent
+    /// `turn_stats` row so the per-agent web UI's `ctx-badge` paints
+    /// real numbers on cold load instead of staying empty until the
+    /// next turn finishes.
+    pub fn seed_usage(&self, usage: TokenUsage) {
+        *self.last_usage.lock().unwrap() = Some(usage);
+    }
+
     /// Record the latest token usage from a completed turn.
     pub fn record_usage(&self, usage: TokenUsage) {
         *self.last_usage.lock().unwrap() = Some(usage);