The best casual games like Harvest Moon are Stardew Valley, Story of Seasons: A Wonderful Life and Coral Island. Below are 7, each with the reason it is here — and, at the end, what filtering to casual costs you.
Filtering to casual means you want something you can put down. That is the whole definition, and it says nothing about how deep the game is.
What you get: A game that fits around a life. Short sessions, save anywhere, no penalty for a week away.
What made Harvest Moon worth playing in the first place is covered on the full list. This page is the casual part of that answer, and only the casual part.
The game that took the Harvest Moon formula and perfected it.
The actual continuation of the original series under its new name.
The most complete modern take, with a bigger town.
Crafting and building rather than farming, same rhythm.
If the daily routine and the neighbours were the appeal.
The closest in tone to the SNES-era games.
For the same slow build of a place that becomes a system.
Momentum, sometimes. A game designed to be left is also a game that is easy to forget you were playing.
Specifically, these are strong answers for Harvest Moon that are not casual games, so they are not on this page:
The full list is on games like Harvest Moon — 9 picks, no genre filter.
Stardew Valley. The game that took the Harvest Moon formula and perfected it.
No. Harvest Moon released on the Nintendo Game Boy, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
No. Several of the deepest games there are — Tetris, Balatro, Into the Breach — are playable in twenty-minute pieces, and some of the shallowest demand an entire evening.
Often the opposite. Many are built around daily timers and streaks, which means stopping does cost you — the one thing a casual game is not supposed to do.
By hand. Each pick was written for the full Harvest Moon list first, on what the game actually does, and this page is the part of that list that is casual — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the casual guide for where to start in the genre generally.