perf(build): skip TS in next build, reduce sentry upload, add CI typecheck (#2782)

Build optimizations (~110s savings):
- typescript.ignoreBuildErrors: true — skips the 79s TypeScript check
  during next build. Type errors are now caught by the check-types CI
  workflow instead.
- widenClientFileUpload: false — reduces Sentry source map upload
  scope, saving ~30-40s of scanning/uploading client-side files.

CI:
- Added pull_request trigger to check-types.yml so typecheck runs on
  every PR, replacing the in-build check.

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: Marfuen

apps/app/next.config.ts

@@ -140,7 +140,7 @@ export default withSentryConfig(withBotId(config), {
   // https://docs.sentry.io/platforms/javascript/guides/nextjs/manual-setup/
 
   // Upload a larger set of source maps for prettier stack traces (increases build time)
-  widenClientFileUpload: true,
+  widenClientFileUpload: false,
 
   // Route browser requests to Sentry through a Next.js rewrite to circumvent ad-blockers.
   // This can increase your server load as well as your hosting bill.