My house is gray, trim is white, mudroom door is white and front door was green (just repainted black). I would paint the mudroom door either the siding color (putty) or the trim color.

All the same color because it's essentially one in the same element. In other words, you can have a door with no side lights but you can't have side lights without a door. That's why it doesn't make sense to paint the side lights a different color from the door.

Snap a photo on a sunny day then use the Sherwin Williams ColorSnap app to play with the colors. I would select a tone slightly darker than your mortar for the garage door and a color slightly darker than your darkest brick for the front door. I would then on the garage door install magnetic faux hinges and windows; this will add detail to the door, like the below house. I know they can be found on Amazon, not sure where else. Before: After:

I like the color of a charcoal roof for your house, and also charcoal shutters. The door should stand out on its own, and could be almost any bright color of your choice. Rusty red. Dark teal, orange, etc. A very pretty house.