Standard spanish is used all around in the sense that: people have known it for a long time. We understand it all. Of course there are localisms, but the same way Andalucia, Extremadura or Murcia speak a very strong dialect, in my area or Valladolid, Salamanca, Madrid or even Cataluña people speak a very standard one. In fact, the areas you said are the most "dialectizied". The rest of Spain is way more standard when speaking it.
Pero no me informo por canales políticos exclusivamente. Sé de lo que hablo, créeme.
Las diferencias entre euskalkis son como las que puede haber entre un murciano, un chileno, un cubano, un colombiano y un mexicano. El léxico puede variar enormemente, incluso las conjugaciones verbales auxiliares (dot/dut/det) pero el idioma es el mismo. En castellano pasa igual con dile/decile al otro lado del charco en el cono sur.
Sobre el uso político, para mí portugués y gallego podrían ser el mismo idioma perfectamente salvo diferencias morfológicas triviales, cosa que ya ocurre de forma clara en la conjugación verbal argentina, chilena y uruguaya.
https://en.wikipedia.org/wiki/Greek_language_question
So regardless of whether there's a "true" Basque language, it certainly could have gone through a period of conscious, top-down reconstruction after some period when middle-class academics (and politicians, usually) who would be interested in either rediscovering or purifying the language, or just plain looking for a nationalist project to rally around couldn't find anyone left who spoke the language at all, spoke it purely enough for them, or even spoke it prettily enough for their image of what the language should be.
I don't know that this happened to Basque, but it happens all the time.