I would do wood moulding as suggested by Fori. Or use plastic and paint it to match the walls. You'll never notice it when all is said and done.

This is what a metal Schluter edge would look like. I would avoid the plastic edging, unless you have a tile with you when you choose it, and confirm they match.

We chose the tile, the grout, and the edge, and did all the work ourselves. The metal edge blends in with the grout, and gives it a clean look. I let the tiler choose the edging in my bathroom, and it's plastic and doesn't really match. Make sure you are the one to choose!!

Yes I agree with the Schluter option as well https://www.schluter.com/schluter-us/en_US/Profiles/For-Floors/c/P-FF

Check out the link above

I had an old house with a bathroom that had Formica half walls with a neat metal strip along the top. That's not the look our poster wants. I think the Schluter on a long half wall would be a bit much. Schluter is best when it disappears.

It sounds like a chair rail is almost what we'd want here.

Thank you everyone for your input. Much appreciated. In the end, we left the top open-edged (it's above eye-level) and along the side we used the glazed edge of each tile. (There was a concern with then having a 'cut' side against another tile, but because my tiles are slightly rustic with imperfect edges it wasn't an issue at all and you can't even tell along the grout line). I'll post pictures once done, the tiler is just finishing up now. But overall I'm very pleased.