feat: add initDispatcher() for eager sidecar startup

The dispatcher was lazy-initialized on first AI request, but a race
condition meant the first call always missed it (dispatcherReady still
false) and fell through to cold per-request Python. initDispatcher()
starts the dispatcher eagerly and returns a Promise that resolves with
GPU status once ready (or after a timeout).

packages/ai/src/bridge.ts

@@ -330,6 +330,44 @@ export function shutdownDispatcher(): void {
   }
 }
 
+/**
+ * Eagerly start the Python dispatcher and wait for its readiness signal.
+ * Returns the GPU status once ready, or {ready: false} on timeout/failure.
+ * Safe to call multiple times -- idempotent if the dispatcher is already running.
+ */
+export function initDispatcher(timeoutMs = 30_000): Promise<{ ready: boolean; gpu: boolean }> {
+  if (dispatcherReady) {
+    return Promise.resolve({ ready: true, gpu: dispatcherGpuAvailable });
+  }
+  if (dispatcherFailed) {
+    return Promise.resolve({ ready: false, gpu: false });
+  }
+
+  const proc = getDispatcher();
+  if (!proc) {
+    return Promise.resolve({ ready: false, gpu: false });
+  }
+
+  return new Promise((resolve) => {
+    const timer = setTimeout(() => {
+      clearInterval(poll);
+      resolve({ ready: false, gpu: false });
+    }, timeoutMs);
+
+    const poll = setInterval(() => {
+      if (dispatcherReady) {
+        clearTimeout(timer);
+        clearInterval(poll);
+        resolve({ ready: true, gpu: dispatcherGpuAvailable });
+      } else if (dispatcherFailed) {
+        clearTimeout(timer);
+        clearInterval(poll);
+        resolve({ ready: false, gpu: false });
+      }
+    }, 50);
+  });
+}
+
 // ── Per-request fallback (original implementation) ──────────────────
 
 function runPythonPerRequest(