Extra part of budget for plumbing and electric?

You don't have to move the circuit box outside of a kitchen. You need a separate circuit for the microwave. Most places want better shut off valves.

You have to move the panel if it is or is going to be inside a cabinet

I've seen in previous Primer 05 comments that it's possible to do a decent renovation for about $250/sq ft. Not counting the cost of appliances, is that true when the kitchen is so small and requires the plumbing and electrical work?

Juxie usually those figures are average for the entire apartment, not just a room.

Juxie100,
Pier45 is right. That is for a complete gut renovation but construction price shave gone up and it is more like $300 sq ft