Tbh a lot of the contrast look is probably caused by the all colour outlines, even though I know you said it is your style, black really helps it. But meh, there your sprites. However, I noticed on things like the Eeevee that you've used the lighter outline on places with darker shadow which again, will cause it to look very off.
Part of that problem however could also be caused by the areas where you haven't mabye put in enough shading imo.
And pillow shading generally isn't used much on official sprites which is why I'd recommend against it. Makes them look a bit less profesional.