I wish you a very successful treatment and speedy recovery, @thistowillpass
I agree that you need to have a conversation about this being non-negotiable. Teens are not naturally wired towards sympathy but if you spell it out, they are old enough to understand and mature and capable enough t do what is needed.
Make it easy for everyone. Have them make a rota on a big piece of paper and stick it to the fridge door. Discuss which days suit each of them best, working with any extra-curricular schedules they have.
They can take turns walking the dog, cooking and doing a cleaning chore each twice a week. That leaves one day a week where you will need outside help - perhaps from your ex, a family member, good friend or home help. No swapping, no delaying, no arguments.
As PP suggested, explain that if they leave it all to you, you will be too tired to give them lifts, to cook or clean.
Discuss ways to make every thing easier for them as well as you. Choose very easy week night meals - pasta and ready made sauce with bagged salad, or baked potatoes with grated cheese, beans and salad, or oven baked chicken kievs/fish with oven chips and peas and carrots. Show them some videos of Jamie Oliver or Nigel Slater or similar chefs who simplify family dinners into recipes that have short, easy prep and cooking times.
Discuss some treats for every one pulling together during a tough time - maybe a family film night or Uber Eats once a week, if all the chores have been done without nagging and complaint.
They'll have GCSE/A level prep at their age (as well as totally essential social lives
) so if you can lighten the load, do. Can you get a cleaner for the next few months so that their main jobs are to keep the place tidy, dog walked and family fed, rather than also cleaning? Could you afford a dog walker, or try to find a willing neighbourhood family who are thinking of getting a dog, who might like to do some regular dogwalks? Or Borrow My Doggy system, if that still exists.