For Y10, I do think he needs to be keeping up as best as he can. As a science teacher, we have picked the bits of the curriculum that will be easiest to learn at home and we'll be setting these for Y10 next term- we won't have time to cover this again in full when school is back on, and bright or not it will be hard to catch up a whole topic next year.
I totally understand all the other stresses going on, and I don't think it's worth getting into an argument about, and I would let him work at his own pace if this is possible with what the teachers are setting. If he needs to take more breaks or doesn't finish everything, then that's fine, but I wouldn't be keen on him not looking at the work at all.
Could you talk to him about the issue without it becoming an argument? Is he feeling overwhelmed with the amount of work? Is he struggling to follow instructions? Is he anxious about other things?
I'd encourage him to contact his teachers to explain any issues he is having- they might be able to break the work set down into smaller chunks, or point out the most important bits to focus on. Maybe if there is a teacher he especially trusts, he could email them about how he is feeling in general?
If he won't do the formal school work set, would he use a site like senecalearning.com to at least cover some of the content?
I do think getting into a good routine will really help his mental health, something like:
Up/dressed/breakfast by 9.30
Do some exercise to start the day (youtube workout?) until 10.00.
Schoolwork 10.00-12.
Lunch 12-1.
Schoolwork 1-3.
More exercise 3-3.30
That's a pretty relaxed timetable which would enable him to still get a fair amount of work done each day. You could build in more breaks if needed and make the schoolwork run a little later?
You could perhaps encourage him to bullet journal and prioritise the things he really needs to get done each day?