How do people not recognize that they’re just as subservient to US capital as the people of the CPP are to socialist characteristics

They recognize it just fine. They simply do not care. Remember a lot of Americans think of themselves as "temporarily embarrassed billionaires." Or their adherence to the white, cisshit, male power structure means they will gladly stamp out anything that threatens that power.

Despite the obviousness of the DNC rallying around Biden during the primary, they still got more people to vote along the party line. They still had to get the majority of votes for Biden and that's exactly what happened because so-called liberals want to uphold American hegemony more than they want healthcare or education.