Replace @nuxt/babel-preset-app loader with explicit configuration

[cnotv]

Description

Loaders currently rely on @nuxt/babel-preset-app, without knowing how these files are loaded or the possibility to update them. Also, this is a leftover from Nuxt which we want to remove. Due to EOM, we want also to replace this with single-maintained libraries.

Context

This issue has been handled separately from #11272 due complexity of the initialization of the app after replacing the loaders. The current state is no error and a white page.