I suspect he will appear very selfish during the recovery time, at least by his normal standards, but this could be linked to the impact caused by the burnout. Those I know who have had this take several months where they require to be left alone as much as possible to slowly recover and return to a normal level of mental health, so if you can, please allow him longer with a lower expectation of what he should be doing in his free time.
Perhaps changing routine will help - getting up early and doing the chores at the same time (or different chores at the same time) will get the work out of the way soonest and let you have the evenings to relax together and enjoy each others company.
I can't offer anything more on this as it could be seen as medical advice and that is forbidden here.
Group activities are probably not a great option when in burnout as the stimulation can be counterproductive.
If you are able to afford it and he is willing then I can recommend working with a psychotherapist to help him develop his own coping mechanisms and communication skills to be a more effective partner and to let him understand his needs better - and then communicate all this to you.
At around £60/hour is is a good investment in my opinion.
In my experience of one failed marriage many years ago and now in my 60s and excellent one, there are times when one person in the partnership is way more functional than the the other, and it doesn’t necessarily even out over time. He may never be as capable as you are, and perhaps you have the better end of the present situation ? You say he is sweet, affectionate and loving, Personally Id take that over him doing chores, dishes, laundry any day
