move pi-mono into companion-cloud as apps/companion-os

- Copy all pi-mono source into apps/companion-os/
- Update Dockerfile to COPY pre-built binary instead of downloading from GitHub Releases
- Update deploy-staging.yml to build pi from source (bun compile) before Docker build
- Add apps/companion-os/** to path triggers
- No more cross-repo dispatch needed

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

packages/coding-agent/src/core/timings.ts

@@ -0,0 +1,25 @@
+/**
+ * Central timing instrumentation for startup profiling.
+ * Enable with PI_TIMING=1 environment variable.
+ */
+
+const ENABLED = process.env.PI_TIMING === "1";
+const timings: Array<{ label: string; ms: number }> = [];
+let lastTime = Date.now();
+
+export function time(label: string): void {
+  if (!ENABLED) return;
+  const now = Date.now();
+  timings.push({ label, ms: now - lastTime });
+  lastTime = now;
+}
+
+export function printTimings(): void {
+  if (!ENABLED || timings.length === 0) return;
+  console.error("\n--- Startup Timings ---");
+  for (const t of timings) {
+    console.error(`  ${t.label}: ${t.ms}ms`);
+  }
+  console.error(`  TOTAL: ${timings.reduce((a, b) => a + b.ms, 0)}ms`);
+  console.error("------------------------\n");
+}