The first thing that comes to mind is Red Star by Alexander Boganov. It is pretty explicitly "about" communism in that it takes place on a communist Mars. It was written in the early 1900s but I think holds up fine.

The Culture series by Ian Banks features a communist-post-scarcity economic society.

Any books in the Noon Universe universe by Arkady and Boris Strugatsky take place in a future Earth where communism has spread over the planet.

Fire on the Mountain (1988) by Terry Bison is an alternate history novel that takes place in an African American socialist republic a century after Harriet Tubman's and John Brown's successful raid on Harper's Ferry. I've read some of it and have been meaning to finish it. I suppose it's quite explicit in its socialism, however.

2312 (2012) by Kim Stanley Robinson is a science fiction novel that takes place across a colonized solar system with multiple POVs. I quite like it, but if you much prefer narrative over worldbuilding then you may not. However, it does fit your criteria better. Socialism appears to be the predominant mode of production, with references to widespread worker co-ops (the author is obsessed with Mondragon), solar-system-wide economic planning, and I don't think money comes up at all... Earth seems to be kind of fucked up though, so I guess you could say it has FALGSC but not FALGEC. Finally, I should note that Kim Stanley Robinson is not a Marxist.

Andromeda Nebula by Ivan Yefremov takes places on future communist Earth. His Hour of Bull also takes place in this setting, although it is more about Earth's expedition to an another planet, where descendants of colonists have managed to preserve capitalism.

These vary in explicitness: ‘what is to be done’ by chernyshevsky, ‘ecotopia’ by callenbach, ‘news from nowhere’ by morris, ‘utopia’ by more, and ‘parable of the sower’ by butler (this one is not about communism, but rather non-explicitly building socialism in a realistic dystopia. It’s a must read). The first four are utopian books because that is my current area of study.

The first few chapters of Cosmonaut Keep by Ken MacLeod take place in an alternate history where the USSR took over the EU. The author is either an anarchist or a trot and the main antagonist is a "stalinist." The sequel is pretty good, the 3rd book not as much.

The novels Singularity Sky, Iron Sunrise, and Glasshouse by Charles Stross take place in post scarcity settings that aren't explicitly FALGSC but pretty close.

Ursula K. Le Guin's The Dispossessed.

It always gets brought up as a book specifically about an anarchist society, but I think that's mostly just because of the more negative connotations of the word "communist" and that most people don't understand anarchism and communism share the same end goal.

There's probably a trove of Soviet fiction literature just waiting to be transcribed. Just sifting through the comments, it seems like a lot of the Western books are more anarchist-y/ utopic (not that the books aren't worth reading, they're probably v lovely reads). It would be nice to find a proper communist fiction book that doesn't have any hint of being ashamed about communism and explores cool themes lol.

While not communism per se, Island by Aldous Huxley is a nice read. It's set on a fictional island that is communist-like. It's pretty utopian though.

Kim Stanley Robinson already got a mention in here, but his "Mars Trilogy" (Red Mars, Green Mars, Blue Mars) is an interesting and often depressing look into how humanity of the 1990s-2000s might've handled international joint colonization of Mars by humanity. It's still largely applicable now days, although the Russians in the book(s) were raised in the USSR.

It's hard to explain the books beyond what I wrote, I think. I'd suggest just start reading Red Mars and if you aren't hooked in the first chapter by the jaded, misanthropic-ish Frank Chalmers then you probably won't like the series.

On a related note, does anyone have experience with BookWyrm?