I can't recommend BANANA FISH enough, though the original manga is more explicitly Marxist with regards to its criticisms of the US government and its anti-communist actions in Europe and Asia throughout the Cold War. The main villains are the Corsican Mafia (and their creation by the CIA as part of Operation Gladio), and the CIA (with its imperialist involvement in Vietnam). The anime modernized it by changing it to the Iraq War rather than the Vietnam War, so not everything makes sense from a materialist point of view in that version, but it's still definitely worth a watch. Heavy trigger warnings for mentions of child abuse (not explicitly shown, but the show doesn't tiptoe around the fact that the CIA and FBI used and groomed vulnerable populations for their experiments), drug abuse, trafficking, brainwashing, basically everything the CIA was and still is up to.

Trigger's shows:

Gurren Lagann is about a double revolution.

Kill la Kill is about a revolution, social norms, and different methods of praxis.

Little Witch Academia has extremely strong class themes.

Promare is about a failed global revolution, followed by the defeat of a fascist.

Miyazaki/Studio Ghibli, he's a communist or at least was. He still holds all the same views he had before the fall of the USSR. Everything he makes is marxist in some way whether he still calls himself one or not.

Akira is set upon the backdrop of an obviously marxist revolution.

Shinsekai Yori has deeply political themes but they don't really start until parts 2 and 3. Any leftist will sympathise with Squealer.

One Piece - This is explicitly a marxist story that is building up towards world revolution. The author Oda has Che Guevara on the wall of his office.

Gundam are not explicitly marxist but political themes lean into marxism at times. Some shows better than others, I'm not a gundam expert.

Revolutionary Girl Utena - about breaking gender standards in society. Queer show.

Madoka Magica - I argue this show is explicitly marxist and the entire relationship between magical girls and the system is explicitly a critique and call for revolution over capitalism.

Deca-Dence - Explicitly marxist show. The ending is cowardly though.

Sarazanmai is Kunihiko Ikuhara's most direct attack on capitalism

Kino no Tabi: The Beautiful World - Start with the 2003 version not the remake. Each episode is kinda independent and explores philosophical themes.

Houseki no Kuni (Land of the Lustrous) - What is depicted is an explicitly a communist society with a communist economy. Show features incredible art, incredible directing, and incredible use of body horror to depict the inner feelings of characters. In terms of modern anime it has done more than anything in the genre to change the way the rest of the industry works by demonstrating what 3d used correctly can do for the genre. This show is a masterpiece and one of my favourites, rewatching it always brings new things to analyse or think about.

Does it get more communist than the anime biography of Karl Marx's life?

Dallos is about a space colony going on strike.

Gundam Iron Blooded Orphans has some good Union activity in it.

Not anime but you should definitely watch Damnation and I'm a Virgo

Squirrel and Hedgehog

You might also enjoy the currently airing Orb: On the Movements of the Earth. It's a tense seinen about a prodigious kid in the 17th century trying to research/prove the heliocentric model while trying to avoid being killed by the Church.

I don't think you can find something explicitly communist in popular japanese media tbh, at best you will get something anti-imperialist like Code Geass or the Stormblood expansion for FFXIV, or something class conscious like Kaiji

gotta shill for Patlabor 2 (the whole franchise is great, although I haven't gotten around to watching the whole TV series yet, but the 2nd movie is the most explicitly political)

Patlabor 2: The "Just War/Unjust Peace" Scene (1993) (or with subs here)

We're a rich country, and what is our wealth built on? The bloody corpses in all these wars... they're the foundation of our peace.

Other countries, comfortably far away, pay the price for our prosperous peace. We've learned very well how to ignore their suffering.

Since no one has mentioned it yet:

Chainsaw Man is a story about how our relationship to capitalism is the same as being in an abusive relationship, Manufacturing Consent is just grooming and that at the end of the day we have to eat the rich. (It's not explicitly Marxist but it's class conscious the same way shows like Parasite or Squid Game are.)

https://en.wikipedia.org/wiki/Kamui_(1964_manga)

ZOM 100: Bucket List of the Dead is a pro-social, class conscious zombie story about a depressed and horribly overworked office worker waking up to a zombie apocalypse and celebrating because it means he doesn't have to go to work anymore, then setting out to do all the things he'd never gotten to do before the world ended because he was too busy working, before it's too late. It also criticizes that and he quickly comes around to "oh, this is actually really empty and reckless," eventually settling on a theme that's something like "even in a hopeless, doomed world, even in the face of calamity, it's important to keep living and helping people and finding joy in life where you can."

It's not explicitly Marxist, but a later arc in the manga does have a character explicitly say something like "Marx said that capitalism's contradictions would eventually lead to its destruction, but here the world has ended and capitalists are still [making horrible stratified nightmare systems based on rentseeking and feeding people to zombies] and people just keep going along with it for some reason." There's also a pretty early panel showing a broken cityscape with no electricity, filled with shambling corpses, overlaid with dialogue about careers that has the gem "100 years ago no one would have predicted modern careers like drone pilot or cryptocurrency specialist."

The whole thing is stylish as hell, with decent themes and a tone that walks a line between dry and bitter sarcasm and wide-eyed wonder. It's a little too soft on the more fucked up places it goes too, but ultimately the main characters are almost pathologically-good-natured civilians trying to survive and lend a helping hand where they can, they're not hardened revolutionaries out to fight for a better world. The manga also has a lot of little filler scenes that are basically just the cast going to [insert famous tourist destination in Japan] and all but soyfacing and pointing at [thing it's famous for] before zombies show up and they have to run away. Some pages have multiple of that gag crammed into their panels for a quick montage.

PlanetES - in the near future the moon and space near earth are colonized. Our protagonists jobs are to deal with dangerous space debris but it’s not a profit generator so they are neglected and underfunded despite everything in space relying on them. Also themes of colonialism and the moral hazards inherent in capital accumulation.

Arakawa Under the Bridge is basically "relationships or: how I learned to stop worrying and love mutual aid".

Its about a capitalist who gets thrown into a more anarcho-* social group and lives there. Its silly and rediculous (and warning theres some homophobia I think, its been a while since I watched it tho so take what I say with salt).