feat: add opt-in anonymous telemetry reporting

Add an opt-in telemetry system that sends anonymised instance
statistics to the public API once per day, which proxies them to
PostHog when `POSTHOG_API_KEY` is configured.

- Add `packages/core/src/telemetry.ts` — `performTelemetryReport`
  and `isTelemetryEnabled`; user and title counts are bucketed
  before sending to avoid exposing exact figures
- Add `getInstanceId()` to `settings.ts` — generates and persists a
  stable UUIDv7 for the instance
- Schedule a daily `telemetryReport` cron job (00:30)
- Add `POST /v1/telemetry` to `apps/public-api`; forwards payload
  to PostHog or returns 204 silently if key is absent
- Add `admin.telemetry` and `admin.toggleTelemetry` oRPC procedures
  for inspecting and toggling the setting
- Expose `instanceId` on `system.publicInfo`

apps/public-api/src/app.ts

@@ -26,4 +26,41 @@ app.get("/v1/version", async (c) => {
   }
 });
 
+app.post("/v1/telemetry", async (c) => {
+  const body = await c.req.json();
+
+  if (!body.instanceId || !body.version) {
+    return c.json({ error: "Missing required fields" }, 400);
+  }
+
+  const posthogKey = process.env.POSTHOG_API_KEY;
+  if (!posthogKey) {
+    return c.body(null, 204);
+  }
+
+  try {
+    await fetch("https://us.i.posthog.com/i/v0/e/", {
+      method: "POST",
+      headers: { "Content-Type": "application/json" },
+      body: JSON.stringify({
+        api_key: posthogKey,
+        event: "instance_report",
+        distinct_id: body.instanceId,
+        properties: {
+          version: body.version,
+          arch: body.arch,
+          users: body.users,
+          titles: body.titles,
+          ...(body.features ?? {}),
+        },
+      }),
+      signal: AbortSignal.timeout(10_000),
+    });
+  } catch {
+    // Fire-and-forget — don't fail the request if PostHog is down
+  }
+
+  return c.body(null, 204);
+});
+
 export default app;