feat: integrate Pi backend and Pi Web

pi-web/app/api/runtime/route.ts

@@ -0,0 +1,23 @@
+import { getAgentDir } from "@earendil-works/pi-coding-agent";
+import {
+  getManagedRuntimePaths,
+  isManagedRuntime,
+} from "@/lib/app-runtime";
+
+export const dynamic = "force-dynamic";
+
+export async function GET() {
+  if (!isManagedRuntime()) {
+    return Response.json({ managed: false, agentDir: getAgentDir() });
+  }
+
+  const paths = getManagedRuntimePaths();
+  return Response.json({
+    managed: true,
+    appRoot: paths.appRoot,
+    dataDir: paths.dataDir,
+    agentDir: paths.agentDir,
+    resourcesDir: paths.resourcesDir,
+    skillRoots: paths.managedSkillRoots,
+  });
+}