Thank you! For that flat cartoony style, here how I like to do it:

Gentler lighting/shadows: For lights, reduce the shadow opacity or remove the shadows entirely. Increase the ambient/background lighting so that you don't have dark areas. Too much contrast/shadow creates a harsh look. You can even remove lights entirely and use ambient/background lighting if you can get away with it.

Unlit/Unshaded stuff: Wherever you can get away with it, use an unshaded shader. This helps make things simpler and quicker to create when 3D modeling so you don't have to worry about topology and how it interacts with lighting, and can just focus on the silhouettes and shapes instead. Use vertex colors, or smart UV mapping onto a color palette texture for coloring rather than drawing colors onto a texture map, to have crisp sharp color regions even up close. Use shader parameters to apply a tint to the overall mesh if needed.

Draw/model by hand: Use OpenBrush in VR and draw stuff rather than model it in a 3D modeler to get more of a cartoony/drawn feel where everything isn't perfect. Then export it and clean it up in your 3D modeler tool. The sheep were drawn in OpenBrush and then cleaned up / revamped in Blender and broken up into their parts (head, body, separate legs), and then animated through code in Godot for random procedural animations that look ok and never repeat - which is important when you are looking at dozens of the character at the same time.

Good idea on using the fan to carry the sheep. I had something like that in the beginning but took it out so I wouldn't be tempted to smack the sheep with the fan. But it is a relaxation game, so if it helps one to relax, then I'd better add that back in.

I drew the sheep in VR using OpenBrush and then edited them in Blender. The OpenBrush concepting helps to give things a quirky organic feel.

Fearing performance issues from having too many sheep, rather than using skeletal/skinned animation, I just separated them into their separate parts (head, legs, body) as plain old meshes and then just coded the walking and idle animations.

I just realized you're the hand duck guy! I knew I saw this game style somewhere before.