No door, but we painted all the trim (baseboard & window) the same white as our cabinets.

What is the trim in the rest of the house? I would think it strange for the trim to be the same as the wall color. I think the contrast frames the window and door, otherwise they might get lost in the paint color. I can't recall I've seen that before. I only recall seeing white/off white trim (or cabinet color like above if a white variation) or natural wood trim that goes with the rest of the house...

I'd paint the trim and the ceiling white because the appliances and sink are white and also because I like a real white next to yellow better than an off white.

You can paint them any color you want. Normally if painted, they are painted a color that can be stable even if the wall colors are changed.

My house is from a time when trim was not painted any "standard" colors, but what the homeowner wanted for that room. My upstairs trim is pine green, bedroom is soft gold, kitchen/dining is off white (same as kitchen cabs) main bath is soft white, laudry is bright white, den and library are stained wood.

Where this causes problems is painted doors. The exterior of my bedroom door matches the trim in the hall, for when it's closed. But when Open I have a white door in a room with pale gold trim.