I'm somewhat new to Vue. But I am wondering what backend to use.
As far as I understood GraphQL should do the trick. But when I was taking the Mastery Courses for free this weekend, I came across Nuxt, which is a full stack framework.
Nuxt is still a vue framework, it uses Nitro to make it full stack. Personally I wouldn't choose an all-in-one framework. The vitesse template shows you can compose most of the same functionality with separate packages: https://github.com/antfu/vitesse#features You can then choose a query library that supports graphsql like apollo or tanstack that fit your needs.
You can do fullstack, just pick and choose the layers in the stack yourself. That way you're in control everywhere, and you can pick the best for your usecase.