Lost in Rain
Brothers a Tales of Two Sons
Lost in Shadow
Attack of the Friday Monsters
NiGHTS Into Dreams
Any Animal Crossing
Point and Click Adventure games. Grimfandango or Journey Down are some of my faves. Zack and Wiki is another.
A Boy and His Blob
Endless Ocean series
Daytona USA (few racing games feel as chill as this IMO)
Shenmue does have combat but sparingly and walking around the small town has always been one of the most relaxing games for me. Just the first one not the sequels.
Toy Commander. Sorta does but it's chill.
Lastly a little odd one but Grandia. Yes it's a JRPG but it's pretty easy and the characters and sense of adventure never let the game dive into that typical drowning in melo drama. It's just one of the best games to give a great sense of adventure.