I would say your screen does not need to available all day, but almost all day.
Take breaks and eat lunch and go to the bathroom, just as you would if you are at a corporate office. If you need to run a quick errand (like pick up the dry cleaning next to your house) during when you normally would each lunch, that shouldn’t be an issue. There’s not the expectation that you would be glued every second to your chair and not take healthy breaks and go to the bathroom and not eat anything.
But don’t be annoying and not available when someone is expecting to talk to you. Just say I am about to grab lunch and I can meet in 30 mins at this particular time and I’ll ping you when I am free. Be communicative.