Animal Crossing, Stardew Valley have a lot of great game mechanics and are also about discovery, trade, and building relationships.
Factorio is probably a bit more advanced, but meets your criteria (except for story, maybe). There is a rabbit hole of games like that to go down.
Assassins Creed Origins and Odyssey have “education” modes that are about exploring the world and not murder.
The Mario-plus games (Tennis, Racing, Party) tend to be not violence oriented, are collaborative, but have super hokey stories.
Old school point and click games are definitely up there (Monkey Island, Myst) as people have mentioned.
Ico and Shadow of the Colossus do have violence and battle as central elements, but not in a COD type of way.
A challenge is that most games rely on competition and conflict as core drivers of both the story and the game mechanics. I think something like Tomb Raider could easily minimize conflict while still retaining a lot of really interesting puzzles, game mechanics, and story elements… sometimes playing that game (and uncharted) you feel like a mass murderer with the body counts you rack up. But other games like Metal Gear Solid are designed to allow you to get through them without needing to kill anyone (subdue/knock out though). It’s also hella hard to do that.
Death Stranding is an interesting one to consider as well. There is some violence and extremely dark themes, but aside from the boss battles it’s really minimal on guns and violence.
Ape Escape for PS1 kind-of fits the mold as well - capturing escaped monkeys is a really fun.
Katamari Damacy (spelling?) is really fun as well- you roll up things under your magic rolling ball becomes planet sized.
The Ace Attorney series is also almost entirely narrative and puzzle.
Factorio is probably a bit more advanced, but meets your criteria (except for story, maybe). There is a rabbit hole of games like that to go down.
Assassins Creed Origins and Odyssey have “education” modes that are about exploring the world and not murder.
The Mario-plus games (Tennis, Racing, Party) tend to be not violence oriented, are collaborative, but have super hokey stories.
Old school point and click games are definitely up there (Monkey Island, Myst) as people have mentioned.
Ico and Shadow of the Colossus do have violence and battle as central elements, but not in a COD type of way.
A challenge is that most games rely on competition and conflict as core drivers of both the story and the game mechanics. I think something like Tomb Raider could easily minimize conflict while still retaining a lot of really interesting puzzles, game mechanics, and story elements… sometimes playing that game (and uncharted) you feel like a mass murderer with the body counts you rack up. But other games like Metal Gear Solid are designed to allow you to get through them without needing to kill anyone (subdue/knock out though). It’s also hella hard to do that.
Death Stranding is an interesting one to consider as well. There is some violence and extremely dark themes, but aside from the boss battles it’s really minimal on guns and violence.
Ape Escape for PS1 kind-of fits the mold as well - capturing escaped monkeys is a really fun.
Katamari Damacy (spelling?) is really fun as well- you roll up things under your magic rolling ball becomes planet sized.
The Ace Attorney series is also almost entirely narrative and puzzle.