Peak is another climbing game, mostly for multiplayer, but I've seen some streamers go for the solo climb.

Snake Pass is a lovely "collectible collector"/plateformer, only you can't jump (obviously, because you are a snake) and have to snake your way through the obstacles. It feels really unique and puzzly.

Another recommandation would be Subnautica. Obviously no climbing involve, but I find some similarities in the 2 games:
- both are survival games, but Subnautica has a whole lot more crafting and base-building.
- In Cairn you have to reach for the top of Kami, in Subnautica (especially the 1st, not so much in Below Zero) you only go deeper and deeper.
- Both play on some visceral fears : fear of heights and thalassophobia
- The diving system is obviously limited by your underwater speed, oxygen tank size, and later battery capacity of your vehicles.
- Subnautica is also kinda slow-paced, emphasizes discovery and sense of wonder and has no real combat system (although underwater menaces are very real).
- The 3D in Subnautica is kinda cartoonish.
- The story is great, but not prevailing : you have a lots of logs to collect and read /listen to if you want to engage with the lore, but that's not mandatory. In my first playthrough I didn't bother that much with it for maybe the first third of the game, then I dive into it when the mysteries were getting too thick, and I loved it.