This sounds so much like both my dcs, especially the younger one. It's not much help to hear that some children are so mature that they can self-regulate their screen time and get brilliant grades without much push from parents, and not sure why there is criticism for needing to have more control on these issues when we all know that children grow up at different rates.
FWIW here are a few things that have worked (a bit) for me:
Screen-free evenings witih everyone in the family joining in. We do this one evening during the week, depends on homework timetable. Last year we did Monday, this year we're doing Friday. I think it just gives them a break from being online all the time & helps them learn to fall back on other resources to entertain themselves. It does cause a fair bit of moaning in our house too, but I think the benefits outweight that.
Handing in all screens an hour before bedtime.
Tightly supervised homework. I know you say your home is very busy OP, but is there any way you could schedule even an hour or two a week when your ds could work quietly downstairs e.g. if your other dcs have evening activities, or could you or your dh take other kids out on Sunday morning for an hour while other one supervises homework? Or could you sometimes sit and read a book in ds's room while he does homework? Otherwise I like Drabarni's suggestion of giving specific bits of homework/revision to do and keep checking that it's done within a certain timeframe.
I think the ways to deal with procrastination vary from person to person, so it's worth thinking about whether there are changes that might help your ds work harder. I say this as a procrastinator myself - I work from home in 20 minute blocks and give myself little rewards in between - quick walk around the garden, cup of tea, couple of minutes on FB, etc. One of my dcs prefers to blast through homework (not very carefully) straight after school to get it out of the way, so I try to get him (reluctantly) to see that as a first draft that might need extra work to finish (e.g. there might be a short paragraph where a page is needed, bad punctuation, or things cut and pasted from Wikipedia). At the moment I check it and tell him what needs more work, but hopefully he'll learn to do this himself. Other dc is more like me & needs 'rewards' for sticking to the task.
None of these is a perfect solution but they've all helped in some ways.