Economy and politics are intrinsically tied to one another, no matter how much some economy masters try to say otherwise. Regulations, tariffs and taxes happen because of political pressure and they all have a very direct and measurable effect on the economy. Democracies may not directly control economies like dictatorships can, but they can and do heavily influence it to work one way or another, via tax or tax breaks, easier or harder credit, etc. Culture also plays an important role, even if the majority of economy academics downplay or ignore it, just like they downplay or ignore the importance of nature, but that's a different discussion.

it was founded as a Marxist state

Alright, can you tell me what are some of the marxist teachings that NK applies to how it runs the state and the economy? Because "being founded as" and "actually run as" are not the same. I mean, it's official name is "Democratic People's Republic of Korea". It's obviously not democratic and barely qualifies as a republic

confusing authoritarianism/liberalism with left/right ideologies

I'm not. Left wing ideology usually leans towards "the govt and economy should work for the good of the people". Communism, which is as "far left" as it typically goes, assumes that the people collectively own all the means of production and government becomes unnecessary. Which leads to the next point

It has public ownership

NK doesn't have "public" ownership, as in, the people cannot say that they collectively own anything, and literally have no say in how anything works, everything belongs to and is run according to the will of the state (or, more accurately, the current leader). Like I said before, not different from an absolutist monarchy. Unless you can argue that the majority of Kim's policies are all for the good of the NK people, he cannot be considered "left".

Funny how you mentioned Spain and Portugal but avoided Italy.

What, you gonna tell me that Mussolini was a far left politician?