[Nuxt] Follow-up tasks

> [!IMPORTANT]
> This is the tracking issue for any tasks we still want to do in the Nuxt SDK. Even tough the SDK is officially still in beta, it's **safe to use it in production**.
>
> General open issues, related to the Nuxt SDK are collected as standalone issues with [Package: nuxt](https://github.com/getsentry/sentry-javascript/labels/Package%3A%20nuxt)

General Sentry Nuxt SDK Tracking Issue: https://github.com/getsentry/sentry-javascript/issues/9095

Overall, the following things should work:
- running the dev mode without problems (but server-side monitoring can be limited in dev)
- building + running the project instruments client + server

```[tasklist]
### Tasklist
- [x] Nuxt 4 Support https://github.com/getsentry/sentry-javascript/pull/13799
- [ ] https://github.com/getsentry/sentry-javascript/issues/14029
- [x] CLI Wizard https://github.com/getsentry/sentry-wizard/pull/719
- [ ] pnpm fix: https://github.com/getsentry/sentry-javascript/issues/14221
- [ ] https://github.com/getsentry/sentry-javascript/issues/13330
- [ ] Nuxt 4: Put server-side config in server and client-side config in app
```