Bitcoin restores the equality in terms of access to the best capital by every person with an Internet access. This might be left-leaning by some definitions. It is libertarian in my opinion, because capitalism is all about property rights, and Bitcoin is the epitome of property rights.
In reality, Bitcoin doesn't care at all about the "rights", it only guarantees and protects access to value. But it can work completely without the help of the legal system.
I agree that Bitcoin has a Libertarian nature though, but this does not make Bitcoin right-wing libertarian, see below. In my opinion it's "neutral libertarian".
Is capitalism (the means of production being property of individuals) left leaning? I don't think so. According to communism, property is owned by the State, and not by individuals. Is leftism a little bit of both capitalism and communism? Never truly understood what leftism and rightism is, to be frank.
"Left-leaning" means basically that every human being is treated equally (egalitarianism).
Capitalism (and of course also Libertarianism or economic Liberalism) can be leftist if everybody tends to get similar access to goods and means of production, even if this means that they have to work for it (but there are no disproportionate difficulties for a social group to access wealth, like in most societies).
If there are elitist structures, i.e. some groups of people (due to religion, ancestry or "caste"/"aristocracy" but also family wealth) are getting disproportional advantages then a system is right-leaning for me. This can be also the case with Libertarianism if only some liberties are conceded, and these just benefit a specific group disproportionally.
Bitcoin does not really conced this kind of elitist advantages, although you could argue that early adopters are a group which is benefitted disproportionally, but that is not defined by Satoshi's code, but by the market structure.
The State has not that much to do with the left/right discussion. Historically many Leftist parties and politicians have sought to use the State and its monopoly of violence to
enforce equality or some form of pseudo-equality where a caste of bureaucrats got advantages (and thus these systems are not really egalitarian). On the other hand, there are leftists like Anarcho-communists ("left wing libertarians") who are as anti-State as "Capitalist" Libertarians.
In general I think Bitcoin could be interesting for some left-leaning groups, mainly those who are close to Left-liberalism/libertarianism and not to "State-enforced communism".
