The clear coat is only on the outside. I doubt that vomit would be acidic enough to cause problems. I don't think that baking soda would be caustic enough to cause problems, either. BTW, how do you kno wit was baking powder? Also, if the baking powder got mixed with the vomit, they would tend to neutraize each other.
In the end, if you can't see damage, it is probably not damaged. The clearcoat would be frosted if it started to dissolve. Put a bright light on it at an angle and look closely at it. The best place to do this is in a garage. If you don't have one, do it after dark. Move your head from side to side and up and down; move the light, too. You are looking for any change in the surface, and you may need to have just the right orientation of light, eyes, and car body to see a change in the clearcoat. Paint damage would be obvious.