In this sense, it does mean more or less "classical liberal": a supporter of market economies, and, more generally, the political dominance of the bourgeois class (as, initially, opposed to the gentry, and as, later, opposed to the working class). It's used today by Internet leftists to include basically all of the mainstream political spectrum, but especially to denigrate "progressives" who claim to have leftist values, but in practice support the status quo.

Actually, remarkably close to the sense of classic liberal.

Not if you mean "as the kids say". Sorry.