Note by @cookingsteak

I had a dream about this DS game that was like Digimon. It was called Monster Gift, and basically you raised monsters in and adoption center so they would eventually be given to a kind owner. The monsters were fully sapient and spoke to you and each other. It was a 3D game so it had that good old DS resolution and sound.
It was like Digimon in that you raised the monsters Tamagotchi style and then could have them fight sometimes. The designs were all very pastel, soft and colorful, nature inspired. Some standouts were a rabbit with four ears, two of which served as extra hands. A bunch of slimes with gyroid faces that evolved into globs and then incarnate forms that changed into stable forms. There was magma, grass, water, ghost, stone, and a couple more. There was a giant green and pink clamshell, I think.
The UI was also a soft wooden palette. It looked like everything was on an wood bulletin board, and had bubbly text on it.