Normally when they are in school the routine is a lot better.
I think you need to accept responsibility for their routine. Some small investments of time from you will probably help a huge amount. Kids this age aren't going to just self motivate themselves all day especially when they've been conditioned to choose screens and to think they rule the roost.
I'd start by making a timetable, segmenting the day into something like:
8:30am breakfast together
9–10:30am school work. If there's none set then I'd be buying some activity books for maths/reading/science of the appropriate stage so that they have something to do.
10:30–midday free time to play - their choice but not screens. Make sure there are engaging things sitting in view for them to choose
midday: they make a simple lunch for everyone (sandwiches, wraps etc.)
12:30: lunch - sit down together to eat
1pm: you go out for a walk/bike/run with them
2–3pm: screen time
3–5pm: free time - no screens
5pm: half an hour of chores
5:30pm: half an our of screens
6pm: cook and eat dinner together. Play a short game together after (like Boggle or Dobble)
7:30pm: upstairs, get ready for bed and they can entertain themselves with books/jigsaws etc. (no screens) until lights out at 8:30pm.
If you can be brave enough to tackle the massive over use of screens you'll probably see a positive change in behaviour fairly quickly.
I'd choose an approach of getting them set up with some new fun activities (magician's set, fimo, Lego, board games). If you can show enthusiasm and find half an hour here and there to sit and do some things like this with them they might start to find other interests.
I do know how hard it is working and looking after children but a little bit of attention really goes a long way (I'm a single parent, self-employed).