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.