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The American use of political terms like liberal and socialist are warped from their original meanings.

Both can mean supporting healthcare for everyone for example. Even though that’s neither a policy following from the theory of liberalism, nor is socialized healthcare dependent on following socialism.

The same is true for progressivism and leftists. All of these terms are often used interchangeably to the previous two.

There’s a deep lack of nuance and specificity.

Actual Marxist leftists and democratic liberals are ideologically opposed to another in many ways. In the US they might agree on better healthcare for everyone and waving rainbow flags. Liberals should be for free markets, (regulated) capitalism, freedoms, etc. A leftist should be opposed to all of these. Freedom to a Marxist means something else than to a liberal.

Nowadays a lot of political discourse across the spectrum is deeply rooted in identity, creating division, virtue signaling, moralist preaching, etc.

Discussion on specific politics and details is often cut short by the above campism and clinging to identities.

This applies to the right and the left equally.

Well... The "wing" of a parliament very roughly represents a political compass. Liberals aren't left-wing anymore by virtue of having more politically left parties that occupy those physical seats today.

It does create a very funny situation like here in Denmark where "Venstre" (literally The Danish word for "Left") is a right-wing political party. More right-wing than "Liberale Alliance" (Danish Liberal Party).

But Venstre used to be the left-wing party when it formed. Since then, green parties, socialist parties, communist parties, and various parties adjacent to those ideologies, have formed to occupy the left side of the parliament seats, pushing Venstre's physical seating position all the way to the right side.

With liberals and moderates being more politically left than them, Venstre now sits right next to the most conservative parties of Denmark. They're still keeping the name, though.

More like the European reality.

Compared to Europe, America doesn't have a left wing. Just a right wing and an extreme right wing.

Liberalism is fundamentally a right wing ideology, it's primarily concerned about the freedom of markets, rather than the freedoms of people, and when it comes down to choosing between the rights of individuals and the interests of corporations, liberals will side with business interests, nearly every single time. Usually, they'll always couch it in more progressive terms, like talking about jobs and economic growth. That's why both mainstream Democrats and mainstream Republicans agree on most issues, because they're both pro-business, pro-capitalist institutions.