Labor theory of value is insanely flawed and has absolutely nothing to do with Bitcoin's Proof of Work.
All value is subjective because it only exists in our minds, all people value the same things differently, and the price is just a consensus between the seller and the buyer. Labor theory of value treats value as some sort of objective physical property, and it fails to describe the reality because it totally ignores how economy actually works.
It completely fails in the case of Bitcoin, because the total network hashrate is driven by the price, not vice versa. Miners add more ASICS because they see big profitability, they never add ASICS hoping that this will drive the price higher. This is because the market doesn't see PoW value as linear, if the network is already secure, the security gains will start to diminish (even though the cost of attack scales linearly).
Labor alone is not the source of value, other people need to view it as useful in order to create value, and this is not a binary value, it's a scale. Bitcoin price increased so much since it's launch because more people became aware of it, more people started to want it, while the supply was decreasing.
I'm pretty sure that Satoshi was familiar with Austrian economics and maybe was even inspired by them, because PoW is based on supply and demand, not labor theory. If Bitcoin was based on Marxist ideas, it would have constant difficulty and constant reward and fixed fees (or no fees).
Multiple false statements. From where do I begin?

PoW is not based on anything other than game theory and mathematics. Nobody designs any thing based on supply and demand, what the hell are you talking about?
Bitcoin is a socio-economic commodity made by labor and it is why it has value and USD has not. Austrian school can't understand why USD is not a commodity and has no value, LTOV can. If price was an existential index of a commodity it wouldn't fluctuate like a feather in the winds of market. Price is a concrete representation of value but is not the value itself. It eventually and in long run acts like an anchor for price.
Bitcoin is an alternative monetary system you can not fool us by giving a neutralized image of it. Cryptocurrency movement is not understandable by fake economists with their original versions being hired and supported by power to say just something no matter what against Marx!
You have no clue: the latest sentence that I quoted from you and bolded above says everything about your naive understanding of bitcoin and Marx and more importantly your biased political point of view that reminds me of cheap anti-Marxist propaganda in the USA in the cold war era.
Half a century is almost passed, there are literally no Marxists for people like you to fight against them and hide your failed economy behind such a
holy war.
And now we have bitcoin that is based on work. You like it or not, bitcoin is based on work and it is the source of its value, you understand it or not, LTOV is the only economical framework available that can shed light on why bitcoin consumes energy instead of following stupid Austrian school advices and let governments to continue doing their job by creating money out of thin air.