Carry per-node emit counts in the live snapshot

The brain graph counts node_executed events client-side and the websocket is
torn down on every shell change, so anything a flow published during the
navigation gap was lost. The bus now keeps a session tally per qualified node
and the snapshot hands it back, letting a reconnecting client catch up.

Both the route and the tunnel connector build that snapshot from one helper
so the portal cannot drift from the direct connection.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01HTsT1isxUjw5gtkJk8WhuA

backend/app/api/routes/flows.py

@@ -730,6 +730,25 @@ def read_message_history(
 # -----------------------------------------------------------------------------
 
 
+def snapshot_payload(controller: FlowController) -> dict[str, Any]:
+    """Everything a client needs to catch up, sent the moment it connects.
+
+    Also sent by the tunnel connector, which serves this websocket inline: the
+    two have to agree, so they build the message here rather than each their
+    own. ``emits`` is what the bus counted while nobody was listening — a
+    client that reconnects between two pages would otherwise start from zero.
+    """
+    return {
+        "type": "snapshot",
+        "values": controller.values(),
+        "nodes": [s.model_dump() for s in controller.node_statuses()],
+        "issues": [i.model_dump() for i in controller.issues],
+        "paused": controller.paused_flows(),
+        "logs": list(event_bus.recent_logs),
+        "emits": dict(event_bus.emits),
+    }
+
+
 @ws_router.websocket("/ws")
 async def flow_events(websocket: WebSocket, token: str = "") -> None:
     """Stream values, node status and execution events as they happen.
@@ -749,16 +768,7 @@ async def flow_events(websocket: WebSocket, token: str = "") -> None:
         websocket.app.state, "flow_controller", None
     )
     if controller is not None:
-        await websocket.send_json(
-            {
-                "type": "snapshot",
-                "values": controller.values(),
-                "nodes": [s.model_dump() for s in controller.node_statuses()],
-                "issues": [i.model_dump() for i in controller.issues],
-                "paused": controller.paused_flows(),
-                "logs": list(event_bus.recent_logs),
-            }
-        )
+        await websocket.send_json(snapshot_payload(controller))
 
     async with event_bus.subscribe() as queue:
         receiver = asyncio.create_task(websocket.receive_text())