Absolutely paint the ceiling black. It looks unfinished as is. It will not make the room look smaller. Might even make it look bigger without the white lid effect it has now. Yes, use the same sheen as on the walls.

Gold mirror and light fixture will look nice in here. I'd get some art on the walls too.

Pls add some photos with the lights on in the room (if you can't install the ceiling light(s) - bring in a floor lamp + a table lamp).

Personally, I think I'd probably color drench the whole room = paint the ceiling + wainscoting + trim. I would paint the wainscoting/trim/inside of door a different sheen than the walls/ceiling.

In the below photo, she used matte on the ceiling, eggshell on the walls, and satin on the picture moulding/baseboards/back of door:

Color is BM Intrigue:

This next photo isn't a powder room - however, it uses BM Intrigue above white wainscoting. The powder room would have a very different feel to it if she had painted the ceiling and the bottom picture moulding/wainscoting white.

BM Intrigue (with a creamy white ceiling and wainscoting) + natural light:

I would definitely paint the ceiling the same as the walls. Powder rooms look better when color drenched.

The powder room looks less “chopped up” with the black ceiling, right? I double down on my vote to paint the ceiling the same color as the walls. Thank you @lisedv for the photos.

Suggest Satin or Eggshell

Use the same metal finish

Yes to painting ceiling black. You have 10' ceilings so the room will not look small with the black paint.

Remember that a dark ceiling tends to look lowered. If that is the desired look then will say go for it.

When just the ceiling is dark, I think it does loo lowere. When a wall and ceiling is dark, I tend to think it looks higher, not lower.