feat: integrate Pi backend and Pi Web

pi-web/app/api/agent/running/events/route.ts

@@ -0,0 +1,56 @@
+import { getRunningRpcSessionIds, subscribeRunningSessions } from "@/lib/rpc-manager";
+
+export const dynamic = "force-dynamic";
+
+// GET /api/agent/running/events - SSE stream of the set of currently-running
+// session ids. Pushes an update whenever any session starts or stops working,
+// so the sidebar never has to poll.
+export async function GET(req: Request) {
+  const stream = new ReadableStream({
+    start(controller) {
+      const encode = (data: unknown) => {
+        const text = `data: ${JSON.stringify(data)}\n\n`;
+        controller.enqueue(new TextEncoder().encode(text));
+      };
+
+      // Subscribe BEFORE taking the initial snapshot so no state change can slip
+      // through the gap between snapshot and subscription.
+      const unsubscribe = subscribeRunningSessions((ids) => {
+        try {
+          encode({ type: "running", runningSessionIds: ids });
+        } catch {
+          // controller already closed
+        }
+      });
+
+      // Initial snapshot so the client renders the correct state immediately.
+      // (A duplicate frame here is harmless: the client just sets the same set.)
+      encode({ type: "running", runningSessionIds: getRunningRpcSessionIds() });
+
+      // Heartbeat to keep the connection alive through proxies/timeouts.
+      const heartbeat = setInterval(() => {
+        try {
+          controller.enqueue(new TextEncoder().encode(":\n\n"));
+        } catch {
+          // controller already closed
+        }
+      }, 30_000);
+
+      const cleanup = () => {
+        clearInterval(heartbeat);
+        unsubscribe();
+        try { controller.close(); } catch { /* already closed */ }
+      };
+
+      req.signal?.addEventListener("abort", cleanup);
+    },
+  });
+
+  return new Response(stream, {
+    headers: {
+      "Content-Type": "text/event-stream",
+      "Cache-Control": "no-cache",
+      Connection: "keep-alive",
+    },
+  });
+}