You are correct, it is not in the splash zone (but is above it). I do notice that when we take a warm shower there will be condensation on the window. Here is a better photo of the location.

Is there tile in the window frame? it looks like there is. If so I would just repaint the window in a good high gloss paint and Caulk the seam between the tile and the wood. That should keep the water out. Just make sure when you notice the caulking starting to crack, in a couple years, that you redo it.

Post some better pictures you’ve taken after the sun goes down, please.

I'd tile it.

That gap in your first picture is bizarre. Does it look like something shifted or was it just poorly done in the first place?

Does the metal trim even line up in the upper-right corner? From that first picture, it doesn't look like it does.

To answer some of the questions. That is not tile in the frame, that is just wood that has been painted (it sort of looks like tile from a distance, which is why I am guessing our inspection missed this). The gap is what I first noticed last night when I was cleaning, I think it is caused by some poorly done work. The trim does not even lineup properly as noted.

As the builder clearly has no interest in dealing with this, I am guessing I will be the one who will have to do the tile work. As I have two large sheets of the matching tile and the window is not too big, I figure I can get it done myself in a few hours.

I will post more pictures once the sun sets (which takes some time here in the South).

Here are some updated photos.

I think your going to have issues with tiling it. It is hard to get a good seal to the wood. You will need to use a sanded caulking and most of that stuff gets pretty hard when it dries. So it will crack and pull away from the wood over time and then water will get under your tile. I still think the best approach is to caulk all the seams really good with a paintable caulk like this https://amzn.to/2KujtFo you can get it at Home Depot. I acrylic latex so it really easy to work with. won't make a mess like pure silicone. Then just paint it with a really good paint.

Does the window open? It looks fixed. It's out of the splash zone so I think a good paint is fine. You might consider an epoxy paint like Zinsser Perma-white

Also make sure there's adequate ventilation so you minimize condensation.