Add exhaustive NATS factorial, MQTT/UDP probes, and optimal-config report.

Compares r=1 vs r=3, file vs memory, reconnect tax, and projects three
HP DL360 Gen10 NVMe + 10GbE boxes. Keep NATS; do not switch to MQTT/UDP.

packages/verae-nats-cluster/scripts/mqtt-probe.mjs

@@ -0,0 +1,33 @@
+#!/usr/bin/env node
+/** MQTT QoS0 publish rate against nats-server MQTT gateway. */
+import mqtt from "mqtt";
+
+const url = process.argv[2] || "mqtt://10.10.10.21:1883";
+const count = Number(process.argv[3] || 5000);
+const size = Number(process.argv[4] || 128);
+const payload = Buffer.alloc(size, 9);
+const topic = `bench/mqtt/${process.pid}`;
+
+const c = mqtt.connect(url, { reconnectPeriod: 0, connectTimeout: 5000 });
+await new Promise((res, rej) => {
+  c.on("connect", res);
+  c.on("error", rej);
+});
+const t0 = process.hrtime.bigint();
+for (let i = 0; i < count; i++) {
+  await new Promise((res, rej) => c.publish(topic, payload, { qos: 0 }, (err) => (err ? rej(err) : res())));
+}
+const ns = Number(process.hrtime.bigint() - t0);
+c.end(true);
+const sec = ns / 1e9;
+console.log(
+  JSON.stringify({
+    mode: "mqtt-qos0",
+    count,
+    size,
+    url,
+    secs: Number(sec.toFixed(3)),
+    pubs_per_sec: Math.round(count / sec),
+    mb_per_sec: Number(((count * size) / sec / 1e6).toFixed(2)),
+  }),
+);