Google intensifies censorship of left-wing websites

No, that's almost completely wrong. Being extremely generous, it could be interpreted to only slightly misstate something that was approximately true in the early 1990s, at the height of the “neoliberal consensus”. At that time, the difference between the (dominant, from Bill Clinton on) neoliberal faction of the Democratic Party and the then-dominant faction of the Republican Party was largely over issues of rights of disadvantaged identity groups (though it must be noted that this was primarily about economic rights, so it is still about the economy) whereas the difference between the progressive wing of the Democratic party and the dominant faction of the Republican Party was more over issues of economic class and structure. (Note that even then, provision of healthcare access was an exception to this, as an economic but not identity-group issue on which both major factions of the Democratic Party differed from then dominant faction of the Republican Party.)

However, that is not because the neoliberal wing is less focussed on economics (neoliberalism, after all, is a label that applies to an economic policy orientation), and with neoliberal economics no longer dominant in the Republican Party, both Democratic factions differ from the dominant faction of the opposing party on core economic issues.

Note that I use “neoliberal” and “progressive” rather than “liberal” and “left” because “liberal" is heavily overloaded in US politics, and the center of mass of the two wings are basically center-right (neoliberal) and somewhere between center and center-left (progressive); there's essentially no substantial true Leftist faction in the Democratic Party.

As far as the outlets you list, Mother Jones is mostly associated with the progressive wing of the party, though that’s far from a perfect alignment; I'd agree that the other two, insofar as they align with either Democratic faction, tend to be more in line with the neoliberal faction.