observability: Sentry is a no-op stub and no @sentry package is installed

apps/web/src/lib/sentry.ts is a stub. Without SENTRY_DSN every call logs to stderr and returns:

export function captureException(error: unknown, context?: Record<string, unknown>): void {
    if (!sentryConfig.dsn) {
        console.error('[sentry-stub] exception captured:', error, context ?? '');
        return;
    }

No @sentry/* package is installed in any workspace package.json, so even setting the DSN would not send anything. The default alert handler only logs as well.

Why it matters

Production has no error reporting. When the worker drops a job or a webhook 500s, nobody finds out unless they are reading Railway logs at that moment. This compounds #182 (a wedged worker still reports healthy) — two independent blind spots on the same service.

Fix

Install @sentry/nextjs for apps/web and @sentry/node for the worker and bots, wire the real SDK behind the existing stub interface so call sites do not change, and route the alert handler to Slack or PagerDuty for anything above a threshold.

Start with apps/web/src/lib/sentry.ts and inspect the workspace package.json files to understand the existing stub interface and available dependencies. Trace its call sites and the default alert handler before choosing the SDK integration points. Done means the web, worker, and bot errors are sent through Sentry and above-threshold alerts are routed to Slack or PagerDuty without changing call sites.