> Harris and Biden are heavily held in contempt by most of the Left.
To be absolutely frank, I don't consider the Democrat party as "Left" in any (traditional?) sense at all, even though it may include Left and Left-leaning elements.
(But then again I don't consider Starmer's Labour as Left either, and one could argue that Labour is more Left than the Democrats.)
The Democratic (not "Democrat", a member of that party is a Democrat, but the party is the "Democratic" Party), and calling it the "Democrat" party has its roots in Republicans deliberately misnaming the party as one of many attempts to devalue and dismiss the Democratic Party. If that's your goal, then please continue. Otherwise, it's like calling an Englishman a Limey or a Pommie just because you've heard others do so.
Otherwise, you're quite correct, in that the US Democratic Party is mostly a center-right party, with it's most progressive/left-wing elements being firmly center-left.