In Starfinder, if I have a computer with the Range Upgrade, does that provide range to all devices connected through Control Modules, or do I have to buy the Range Upgrade multiple times -- once per device?
You dont have to upgrade your devices
The Range computer module (pg. 216) says:
The range upgrade provides a secure, remote connection to a device which allows it to be controlled from a distance. Without this upgrade, a computer must be physically connected to the devices it controls with its control module.
So, this upgrade and the control module is all you need to remotely control devices connected to your computer. The control module allows you to send commands to other devices, and the range module increases the distance the signal may reach.