they can make copies of your software whenever they want, it's their hardware. They can block specific software from running, etc. Their hardware, their policies. It's certainly not your rules. Buy a Notebook!
Hmm, does this extend to the Internet connection? Would using a work wifi for your side project mean they can claim to own it? What about public wifi? In order to keep your project safe, do you have to get a cellular connection and VPN into your home network?
Sniffing into any type of connection is feasable, expect if it's your own (Mobile Network). But they can still control your notebook how they want, take screenshots, etc. Because the software within a notebook only needs internet connection, the control, policies, etc it's centralized and pushed to the software in your desktop with any internet.