You're talking about Democrats and Republicans, whereas I'm more interested in the underlying cultures of liberalism and conservatism. The DNC is a centrist institution, whereas the Republican Party is far-right, especially under Trump. There is no effective left-wing representation in the US, and it's not because the whole country is center-right, contrary to what you say in your last paragraph.
If you poll Americans on the actual policy issues, most agree with liberals and progressives. But because of the culture war and the muddying of the waters, you can't out yourself as a liberal or as a progressive without violating a taboo. That identity politics is purely a matter of rhetorical signalling, not a reflection of what most Americans believe when they stop and think about it.
So I agree that the corporate media side with the Democrats, but that has nothing to do with progressive values. Both the media and the DNC are centrist, neoliberal institutions. What does it matter whether Democrats outmanoever Republicans if Democratic politicians don't listen to their constituents and vote with the Republicans, as you point out? What does it matter when they betray their alleged progressive values, as Bill Clinton did when he triangulated instead of using his bully pulpit to sell left-wing ideas, or as Obama did when he bailed out the banks and not Main Street, or as Hillary Clinton would have done if she had been elected? That's all a tempest in a teapot.
Biden is using the old centrist trick of having one or two Democratic congresspeople fall on their sword and side with the Republicans to tank progressive legislation. The DNC demonizes Manchin and Sinema, but that's just political theater.
My point, then, is that Democrats are crafty only at hiding their double-dealing, because they're incompetent at the primary political task, which is to sell your agenda. The Democrats have no alternative agenda because they're centrists and have abandoned the progressive left-wing. They can't sell anything, so they just disguise their complicity with the neoliberal, far-right Republicans.