This wouldn't be "illigal", but if that's the case Annas Archive should be "fine"... (I know that they are distributing, and this is the fight)

I don't know much about European law, but redistribution changes things a lot here in the US. At least here, it then gets into copyright law, and you'd be reproducing copyrighted works without authorization (the Internet Archive attempted to get around this with books by getting legitimate copies of the books, digitizing them, then "lending" the digital copies of those books).

So if I prefer to download the Anna's dataset instead of scrape myself, would this be illigal?

No idea in Europe. In the US, it might be, depending on what the contents of the work are. I believe Anna's Archive would count as piracy in this case, though scraping directly from Spotify might not be because they are redistributing the music with authorization from the copyright holder. It gets pretty confusing, honestly.

Regardless, if you aren't doing things at large scale, even if you are breaking a law by downloading pirated content, it's unlikely anyone will care. People usually only really start caring if you start redistributing stuff, so as long as you aren't hosting what you're scraping, you're unlikely to run into any trouble.