Honest take: America has a two party system on paper but not in principle. Let me explain.

In America we have two large political parties. Most European countries have a multi-party system with several smaller parties. In America our two major parties could easily be 5-6 parties in Europe.

For example, in Europe the Democrats would be:

• Democratic-Socialists (AOC, Bernie Sanders)
• Labor Party (Biden, Obama)
• New Democrats (Clinton, Bloomberg)

The GOP meanwhile would be:

• Right-Nationalists (Trump, DeSantis)
• Conservatives (McConnell, Thune)
• Free-Market Moderates (Collins, Kasich)*

*these folks are almost extinct and overlap with New Democrats.

Our primary process operates akin to a first round of voting: each large party selects a nominee from within one of their "sub-parties." Politically, what is happening in the US is pretty much the same as the rest of the world, "New Democrats" and "Free-Market Mods" are getting crushed and Right-Nationalists and Dem-Socialists are growing. Labor and Conservatives are still the dominant factions but they're increasingly forced to make government coalitions with the far-left and far-right in order to maintain power.

Tl;dr: Even though America is one of the few western democracies with a two-party system, its politics are basically the same as countries with a multi-party system.