So, there's not really anything like a 3D painting machine/robot like I think you're looking for, but there are printers that do fine detail with actual paint, usually oils, but not on 3D materials.
I found a thread that talks about canvas printing about 8 years ago, along with a couple of videos that show current machines doing just that, but that's still not what I think you're looking for.
There are also CNC machines that print with enamel paints, but these are usually for 2D again, and not very precise, as they are used for lapel pins that have cavities to hole the paint while it dries. I'm sure something like this could be used without the cavities, but you'd have to do a lot of testing to make sure the paint stays put or mixes as you want it.
Just like the oil printers, these enamel printers are likely very large and costly.
What might work for you is hydrodipping. There's a variety of methods to this, but one company has done a bunch of research on this and can do extremely accurate detail printing to "paint" 3D objects. The below video shows a variety of these hydrodipping techniques, but I've skipped to the most relevant part.
Here's the original video of what I think you're most interested in. It's not 3D printing in the way most of us think, but it's definitely a fantastic outcome.
To explain, if these videos are ever deleted: detailed prints are made of a 3D model to color it exactly the way it needs to be, sometimes using multiple steps and computer positioning to get the object colored/"painted" correctly and seamlessly. One part of the video shows how the software can accurately make straight lines on a human-contoured face mask, while another part shows how a blank, fully 3D cat model can have spots or stripes added in 3 steps with the seams being completely invisible as well as it detailed enough to be mistaken for a real housecat beyond first glance.
As it turns out, you can do (some of) this yourself. After doing some research, I've found that you can actually get blank (instead of pre-printed) films and use an off the shelf printer, as long as it meets certain requirements. (I'm not recommending a site, brand, or anything else, this is just the first/only option I can find. If you do more research, I'm sure there's more options out there.)