That’s new to me. If you’d ask me which US party plays identity politics, I’d say the Republican party and Trumpists especially. In the European Parliament, until recently the parties that play identity politics were even united in a block called “Identity and Democracy” (they now reorganised under the name “Patriots for Europe”). They are conservative nationalists. You’ll find Orbán, Le Pen and AfD here (basically friends of Trump). Parties in this block tend to be shunned by other parties in national government coalition formations, unless they grow so big that they actually win national elections.
“Classical liberal” parties in Europe call themselves just “liberal”. In the European Parliament they are united in the block “Alliance of Liberals and Democrats”. They are socially progressive (or at least not conservative) and economically centre-right to right-wing (accomodating big corporations rather than workers and favouring less market regulation). I think only conservatives and nationalists would call them left-wing. You’ll find politicians like Rutte and Macron in here.
I’m not sure what “leftist” means in the US nowadays.
If “leftist” stands for politics represented by Berny Sanders, I think it coincides most with social-democrats in Europe (united in the block “Socialists and Democrats”), who are economically left-wing (accommodating workers rather than big corporations and favouring more market regulation). You’ll find Olaf Scholz in here.
If “leftist” stands for politics represented by Jill Stein, I think it coincides most with the greens in Europe, who are socially progressive and economically centre-left to left-wing. These parties tend to be too small to win elections here, but they may be part of government coalitions.
I think Joe Biden was mostly like the christian-democrats in Europe: socially centrist to conservative-leaning and economically center-right. In Europe, Angela Merkel and Ursula von der Leyen are in this camp (and also Friedrich Merz who may win the upcoming elections in Germany).
I’m not sure in which European block Kamala Harris would have fit best. I’d guess she is a bit less conservative than Joe Biden, but still within the christian-democrat range (though she’d probably get along just as well with Rutte and Macron as with von der Leyen).