Sacred Cat Island

Sacred Cat Island is a mysterious cozy story about family, in particular brothers. Rowan, his brother, and their dad move to an island that seems to follow its own rules. There are at least as many cats there as human residents, along with mysterious spirits, magic, and niche technology.

The game mechanics includes a quest system which largely works as a chore and request list. Everyone has inventory slots equal to their age in years, so Rowan can carry thirteen things while his brother can only carry ten. Stats are displayed at the start of each day but aren't really relevant. Rowan's empathy might increase when he showed empathy the previous day but you could figure that out from the prose.

This is a kid-appropriate book that's also enjoyable for adults. The Ghibli comparison in the blurb is very apt.