Gate live feed staleness and isolate Next dev artifacts

- delay stale status for paused live feeds before surfacing disconnects
- keep `next dev` output separate from production build artifacts
- add coverage for the new live-feed stale threshold

apps/web/next.config.mjs

@@ -0,0 +1,16 @@
+import { PHASE_DEVELOPMENT_SERVER } from "next/constants.js";
+
+/**
+ * Keep dev and production build artifacts separate to avoid chunk/runtime
+ * mismatches when `next dev` and `next build` are run in overlapping sessions.
+ *
+ * @param {string} phase
+ * @returns {import("next").NextConfig}
+ */
+export default function nextConfig(phase) {
+  const isDev = phase === PHASE_DEVELOPMENT_SERVER;
+
+  return {
+    distDir: isDev ? ".next-dev" : ".next"
+  };
+}