Left is an ideological slant, not a political party. The left, by definition, cares about the poor and working class.
AOC and Bernie are Leftists. The policies they advocate for are left policies.
The corporate democrats (Biden, Schumer, Pelosi, Obama) are center-right. If it was the 80s, they would be considered conservatives.
The Democratic party started a shift to the right under Bill Clinton, and they have been moving right ever since. The more the republicans move right, the more the democrats follow.
Biden doesn't give a crap about sjw issues. His people cant even get him to apologize for the 1994 crime bill and the effect it has had on african-americans. He doesn't believe in anything the left advocates for. Hes basically a 1980s republican.
His politics would be considered center right when compared with other developed, western countries; in some countries he would be considered far-right.
Until the progressives take over the democratic party, which i believe will happen eventually, calling the democrats leftists is an unrealistic scare tactic.
The democratic party hates the left so much that they funded primary challengers to every leftist in office this cycle after making a rule about not challenging incumbents.