Your employer can install monitoring software on the employer-provided computer to monitor what happens on that computer. Several court cases have established pretty clearly that monitoring the computer they own is within their rights—exactly BECAUSE it is watching computer hardware that they own. But your question is asking whether they can monitor what is happening on your personal laptop, on the same LAN as their employer-provided computer.
ОГЭ-3104. Задания 18-26. When I came into the room, my computer was on. It worried me since I ___NOT/REMEMBER___ switching it on. "My computer's on but I always switch it off before leaving home."