I don't know what kind of tech stuff you have, but since you can run ethernet (or better, fiber) to the shed, you could keep most of it locked in the house and just walk out with your laptop to your workspace each day.

Monitors are relatively cheap these days, you can get a name brand 32" 4K monitor for around $300 - if someone busts in and steals it, the door/window repair will probably cost more than the monitor.