It Could Happen Here is the closest thing to a proper US news podcast like OP wants, but people have already mentioned them and the other Cool Zone shows (Behind the Bastards, Cool People Who Did Cool Stuff, Hood Politics if you don't mind someone who's a little more moderate)

Anyway, here's some suggestions I didn't see on here:

Jacobin's The Dig - A fascinating interview podcast with lefty scholars. If someone publishes a banger of a book on Verso or Haymarket, this is where they'd want to interview. Contains a wide variety of perspectives across the left. Some folks really dislike the host's voice--he just naturally sounds like Roman Mars or Welcome to Night Vale, very quiet and buzzy. I've gotten used to it, and funnily enough he sounds way better when he interviews in Spanish. Prof. Jenny Chan's interview is a little difficult to listen to because her accent can be hard to parse, but I really appreciate her written work demystifying the exact ways the Chinese captive union system screws over workers.

Trashfuture - Extremely funny! Funniest podcast on the list, honestly. Centers on UK politics and the absurdity of the startup tech industry. A lot of their deeper analysis derives from Marx, but I wouldn't call them tankies. They've been pretty okay with criticizing the Soviet Union. Mostly it doesn't seem to come up very much.

Well There's Your Problem - Again, quote funny! A dark-comedy podcast with slides about engineering disasters. Consistent themes include "maybe the corporate profit motive itself is murdering us" and "railway drivers should be treated about a billion timed better." One extremely angry anarchist, two vague Marxists, again all pretty happy to criticize the Soviet Union.

Lions Led By Donkeys: A dark-comedy podcast about military disasters. The main host is Joe Kassabian, an Armenian-American with a degree in genocide studies, a former tank crewman, and an anarchist who's very, very happy to be explicit about his hatred for red-flag authoritarianism. The only time the USSR gets positive press on there is specifically when they're fighting against is even worse (Nazis or the Black Baron, mostly.) He's literally done series on the Soviet-Afghan War, the Winter War, etc. and doesn't shy away from discussion of Soviet atrocity. Very much a "I can hate all of you at the same time" sort of guy.

One Big Podcast, Laborwave Radio: Podcasts about the labour organizing movement mostly from a syndicalist perspective. Very in favor of grassroots worker self organization, skeptical of vanguards. IWW members run the first one.

Work Stoppage: Haven't listened to a ton, but it's pretty similar to the above, focused mainly on strike news.