Is Stream is intended as a basic programming paradigm every Java programmer should use often, or as a performance feature for senior software enhancers, that should be avoided?
I think there's another option that you are not seeing. The primary benefit of Streams (in my humble opinion) is that it's a paradigm for concurrent and parallel algorithms that is much easier to get right.
That is, it's not intended to replace loops in general (although this is a somewhat popular opinion.) But it's not really intended only for experts either. It's intended to allow average developers implement approaches that in the past, only experts could manage.
To this point, a lot of people will use parallel stream to implement multi-threading. This can be fine and it might even lead to an optimal solution but it's actually much less sophisticated that the existing concurrency libraries. And I don't mean just that the code is simpler to write. I mean that the capabilities of the concurrency libraries offer a vast array of design options beyond what the streams API provides. The problem is that you need to have a really strong understanding of concurrency, the Java memory model, and an extensive library.
So ultimately, I don't see streams as an advanced option but one designed for beginners.