I would be checking with the school first to confirm no tests etc on that day, or is it PE day or a day when he has to be in class with someone he doesn’t like or has been giving him hassle?
You need to look at things like is he getting enough sleep, down time generally (including not being on screens too much), eating well etc
Then I read;
“Well he has sports on Saturday too, and Sunday we're usually busy with friends so he gets days off school but not exactly relaxing doing nothing days, usually.” You honestly need to review this, down time is VERY important.
I am firmly of the belief that one of the reasons our dc are struggling with their Mh is they’re not encouraged to properly relax.
It is a skill, one I have not mastered and I suffer greatly with anxiety, my parents too had us doing something every day and talking to them now they now regret this, my sister also has an anxiety condition and my brother is a total adrenaline junkie and stops for nothing, he’s also in a high stress job, he’s not had definable problems as yet but I worry he’s headed for a crash at some point as I don’t believe that is healthy or sustainable.
You NEED to have a schedule for your ds (actually for the whole family!) that includes at least one down day a week. Especially as it sounds like he has a pretty full schedule through the week and as he goes through high school years the stress will increase and he’ll have more homework/study to do.
Teaching him to have a healthy life balance is just as important as educational achievement and indeed can help with educational achievement.
“Doing jobs” with you is also not the answer - you’re punishing him for being honest and admitting he needs some downtime, ok he went about it slightly wrong but you’re massively missing the point - he needs a REST. And not just this week every week.
Knock the Sunday stuff on the head - I’d suggest for all of you, everyone needs a quiet day once a week.