The first games that popped into my head were Forager and Outpath, though these arent so much community building type games. They are more just something cute to relax to. They have farming and resource collecting and honestly play more like an active idler game than anything. Another game ive sunk tons of time into that kinda meets your requirements is Banished. Its just a medieval city builder game but it is deceptively hard to get a good balanced town going which can be pretty rewarding in itself. Theres no money per se but you do have to manage resources. Theres bartering in the game but you use your resources like crops and stone and stuff.

Martian hedgehog in a tuxedo riding a motorcycle

Just to prove your point I fed that into an AI (dreamshaper 8). no other prompts or anything, and this was the first image it generated.

Yeah i picked up quite a few tips for generating good AI porn in this article. Im still not sure if this was satire or not. it basically gives you step by step how to do this.

Nova Drift is great! Easily one of my top played games.

Rogue likes usually have very little story getting in the way. Binding of Isaac, Slay the Spire, Nova Drift, Darkest Dungeon are a few of my top played. I also really enjoy the make your own adventure Creative Survival type games like Minecraft, Astoneer, Terraria, Starbound, Empyrion Galactic Survival etc. City builders, colony sims and Farming Sims are always a good choice too. Some of my favorites are Cities: Skylines, Banished, Timberborn, Forager, The Anno series, Stardew Valley. Then there’s the pure building games. I really enjoy just building stuff and testing my creations out with games like Scrap Mechanic, Instruments of Destruction, Main Assembly, Cosmoteer, Reassembly, Kerbal Space Progam (the first game, Id wait on the second until all the bugs are fixed). Hack and Slash ARPGs are always fun for turning the brain off and most of them dont have a ton of story, save for a few cut scenes here and there. Path of Exile, Torchlight, Diablo 1 and 2 (I don’t like 3 and 4 personally) Grimm Dawn, Cronichon, Fate, Last Epoch are some of my favorites.