https://www.econlib.org/library/Enc/bios/Marx.html
The fact of the matter is that Das Kapital is a foundational text in economics; it provided an analytical framework and an early prototype of rigour (before the introduction of mathematical formalism) that would influence just about every clade of economics that followed.
Not accusing you of intellectual sophistry, but the sentiment that Marx isn’t an economist is seen as rather glib at this point.
Marx was basically just inspired by French Revolution idea of "Liberty, Equality, Fraternity" and dismayed that it didn't work out. He came to some real insights about why capitalism doesn't achieve that vision. He changed his views over time and wrote strongly about cases where he was wrong. He didn't want anyone to idolize him in some static way or be "Marxist". He actually wasn't prescriptive, he didn't say what to do or how to structure a socialist society. He mostly diagnosed problem patterns in capitalism without proposing what the alternatives should be. Or so I've heard, none of this is my original insights or understanding.
Of people who are "Marxists" by self-description, some have been dangerous and destructive, but there are various versions and they often abhor each other. The worst of them are just as self-righteous as the worst of the Austrians.
FWIW, I think the Austrian models almost all have some truth in them. The problem is how they treat them as complete and dogmatic. They think they have it all figured out, and so they just take any situation and insist that their simplistic models are all there is to it. As a snarky critique, I think the Austrians just believe Wikipedia doesn't exist — or maybe they think it exists precisely because of the lack of government intrusion or something. They just have no insight, no model, no perspective of value on how it is that Wikipedia does exist. They are more interested in their models than in human beings (well, to be fair, I think that's similar for mainstream economists too).
I’d be most interested in any socialist schools which explicitly reject the labor theory of value, at least in its original form, and factor in the importance of price discovery and value added from intellectual labor and competent social organization. I’d also be interested in schools which, to the extent they have any recommendations about different ways of organizing money more reliant on social institution, think in game theoretical terms about how to properly balance the incentives of those social institutions and prevent corruption. At that point I suppose it’d be less about economics and more about politics, but what characterizes most socialist schools of economics is the call for social institutions to regulate run away effects of capitalism described by the theory, and I’d be interested in how such institutions might be constructed to be resilient against both stagnation and corruption.
(Note, by the way, that this should account for all labor involved in production, including management. The common objection to charges of exploitation is that business owners do create value, and it's valid - to the extent that do, in fact, create it, as opposed to contributing resources that were acquired through similar exploitation from some other creator. Thus, a business owner who is not involved in any managerial decisions, but rather delegates it all to a hired manager, derives their entire income from exploitation; but for a manager-owner, the part of the income that they would receive for the same performance as a hired manager cannot be considered exploitation.)
Note that LTV is not necessarily a leftist thing, at least as "left" is usually understood today. For example, Lysander Spooner promoted policies, many of which would be considered radical right-wing libertarianism today - but he based it all on his understanding of LTV and ownership of wealth that one produces.
It's also not contradictory to price discovery via markets. Left-wing libertarianism includes free market variations thereof. In fact, some of them emphasize the free market as the foundational concept for a truly egalitarian society, and criticize capitalism on the basis that it is anti free market, and this is exactly what makes exploitation possible to begin with - see e.g. https://en.wikipedia.org/wiki/Free-market_anarchism (but keep in mind that not all left libertarians who subscribe to such ideas are anarchists).
Also agree about it not being a left wing thing and acknowledge that left wing ideas are all not anti free market.
Skimming https://en.wikipedia.org/wiki/Labor_theory_of_value#Karl_Mar... and https://davidharvey.org/2018/03/marxs-refusal-of-the-labour-... and such trying to make sense of the "Labor Theory of Value" and Marx, it seems clear that Marx never even supported the idea let alone had it as a foundational principle. But I find trudging through what Marx actually said or wrote not enjoyable or worthwhile generally.
In the end, it doesn't matter what Marx said or not, what matters is whether specific ideas have merit. I'm pretty sure I would not agree with everything Marx did actually say. The point is that it is completely irrelevant who said something, which is why the trend to label the source as a way to dismiss things is such a problem intellectually.
I haven't heard anything from Varoufakis that seems like BS along the lines of Labor Theory of Value. Everything I've heard from him is pretty solid. But that doesn't mean I stand by anything you ever get from him. IMO, it's useful to have good sources, but not so useful to make a big deal over aligning with any particular dogmatic school of thought. Making up one's mind to be a somethingist is a way to get away from curiosity and feel like you just already understand everything. The utility in such labels is just to help communicate in cases where shared label understanding actually exists.