I‘m not sure what you mean by a u-shaped Schluter edge. Do you mesn their rounded Rindec trim. i dont think that is the best look. I used Schluter’s Quadec square edged trim along the vertical of the tile behind my cook top and I sure it would work along the edges around your window. Here is a close up pic of my tile with the Quadec

Here is the same trim horizontal on my daughters bathroom backslpash

Schluter trim comes in various finishes and colors. The trim does need to be installed before the tile. There are instructions on Schluters website

I’ve used a small profile pencil tile in a similar installation. this pic has a large pencil tile border.

For me, the bullnose is not coordinate. Maybe try some other material like tile as the above mention.

Do a mock up and folllow your gut

I did choose a white schulter that I feel don't look bad with the tiles but thinking about how it'll frame the bottom half of the windows which looks like a "u" might look a little funny? Not sure if that'll stand out too much..

It’s a small piece in the overall design, so i don’t think it will stand out like you think once you’ve installed it and put the tile in.

IMO do not try to match schluter to tile color it almost is invisible as shown so I just use either the satin finish or the shinier one with any tile.As for where the tile should go I would need to see the whole space I very often like the backspalsh to end under the window

I originally wanted it to just go under the window but then the stove side is pretty much the whole under cabinet so felt it would be weird to cut it short on one side.

I agree, the tile needs to go to the bottom of the cabinets.

Can you take more pictures?

I wouldn't stop it at the cab. Take it up four or five more rows so that it ends at more like halfway up the window. If you end at the bottom of the cabs it makes too strong of a line at that one level. I prefer the interest of it going up aways past the bottom. How high is it going behind the range?

I agree about using the satin finish rather than white schluter. I like the finished edge of schluter over just the tile. Think about wiping down that window sill if it's just tile/grout. Yuck.

Not sure if I’m too late. But maybe take the tile to the ceiling.

I would run the tile further up the window so that it matches the height shown under the hood. I like a crisp line so I would do the schluter.