Updating the `with-sentry` example with latest dependencies versions, new feature docs, and also converted it to TypeScript.
## Documentation / Examples
- [x] Make sure the linting passes by running `pnpm build && pnpm lint`
- [x] The "examples guidelines" are followed from [our contributing doc](https://github.com/vercel/next.js/blob/canary/contributing/examples/adding-examples.md)
Co-authored-by: JJ Kasper <22380829+ijjk@users.noreply.github.com>
