I find it funny you claim there is clearly no debate while having a debate about this. The reason the person linked that article because of a different section:
Unrelated to the economic philosophy described in this article, the term "neoliberalism" is also used to describe a centrist political movement from modern American liberalism in the 1970s. According to political commentator David Brooks, prominent neoliberal politicians included Al Gore and Bill Clinton of the Democratic Party of the United States.[48]
Aha! You might say, it clearly says it is unrelated to the economic philosophy, but the point is that the word can often refer to different things, including Democrats.
Here is another quote from that link:
Neoliberalism is distinct from liberalism insofar as it does not advocate laissez-faire economic policy, but instead is highly constructivist and advocates a strong state to bring about market-like reforms in every aspect of society.
Sounds a lot like the Democrats to me.
As for your talk of comparing European liberals to American liberals being "propaganda" I disagree. I don't know if this specific movement in lemmy that you speak, but I don't think it is propaganda to show that one could want to shrink a gigantic government to medium one (European liberal) and they would be the same as someone who wants to expand a small government to medium one (American liberals). Healthcare being an obvious example here: the United Kingdom wanting to privatize NHS could be considered similar to Democrats who want to just regulate an already privatized system. The end state is the similarity not the action taken to get there.
I think this is an interesting discussion and am not trying to prove that European libs are the same as American libs, just proving that there is clearly debate here.