Anything and everything you do on a work computer can (and often will be) monitored.
Only use it for things that you would be comfortable doing with your boss looking over your shoulder.
Give them no reason to dig up dirt if they eventually want to fire you. "Sorry, we have to let you go as you used company property to order lunch way back in 2016". If you think that's paranoid, I'm speaking from experience.
Don't build some software that you are going to sell privately because the company can claim you did it on company time and hence it's company's property and not yours. Just my thought. I'm not expert at the leaglities
Generally speaking, just do work on your work computer. There has been at least one judicial ruling that holds that anything you do on employee owned equipment or networks can be monitored. Save the HN and social media for your phone. Don’t ever connect your personal phone to your employer’s WiFi. If you need your office email on your phone, ask for a work phone or use an old phone.
Give them no reason to dig up dirt if they eventually want to fire you. "Sorry, we have to let you go as you used company property to order lunch way back in 2016". If you think that's paranoid, I'm speaking from experience.