I don't think so. Yes, Democrats (and American progressives in general) don't emphasize socialism as much as the traditional left or some European parties. However, they're generally still sympathetic. Moreover, while American progressives don't worry so much about economic egalitarianism, they very strongly believe that minorities earning less than whites, female earning less than male, etc. is wrong, and are willing to enact things like reparations, affirmative action,and the like to counterbalance that. In the ideal progressive utopia, CEOs would still be paid hundreds of times more than the average worker, but representation of minority race, female, non-straight and trans people among CEOs and other prestigious positions would occur at least as much as their representation in the population, regardless of their ability, and if cis straight white males are represented less than their proportion of the population, that's just gravy, and maybe justified revenge for their dominant position in the past. In fact, wokism is even more egalitarian than Marxism - the latter says from each according to ability, to each according to need, but it was generally expected that the jobs requiring higher ability would be staffed by people of higher ability.

In general, it's obvious that identity politics forms the core of the political class of today's Democratic Party (especially the young), and equally obvious that America is the innovator that other progressive parties follow in this respect. America also has thrown itself into gender politics with particular enthusiasm - gender transitions, even of minors, are a cornerstone of American progressivism today, even as progressive European countries have rolled that back to an extent.

I will concede that Europe leads in the other main aspect of current-day progressivism, the Green movement, although American progressives are avid followers.