Hi OP,
You definitely sound depressed. That black and white, all or nothing thinking is a symptom.
You can and will recover, and when you do, you will realise you are not a waste of space. You have adult children. You kept them alive, didn't you? Even if you weren't the best mum ever (who is?) you successfully reared them to adulthood. That's all the animal kingdom does and they don't feel guilty.
You are allowed to be sad that your relationship ended. And now is hardly the best time to try and get over it, as you don't have the opportunity to go out and get involved in activities that take your mind off it. Lots of us are stuffing our fat faces without the excuse of a relationship breakdown. Lockdown is excuse enough for many of us. 
Be nice to yourself. You don't have to want to be nice to yourself. You just have to do it. Daily bath or shower. At least 5-a-day fruit and veg - ideally 8-10. And some good lean protein. Then if you want some comfort food on top, at least you have had all the nutrients you need.
Do you know the 9-box trick to getting your life on track. Draw a large square and divide it into 9 smaller squares. In each, put an aspect of life. You must include Community Service in one and Health and Fitness in another. Apart from that, you can put what you like - separate out Family, Friends and Romance into three separate boxes or put them all in one under 'relationships'. maybe include Work/Finance, Fun or Rest & Relaxation; Study or Personal development etc. Add Faith or Spirituality if you believe, or Nature/Ecology if you don't etc.
Then make a list of some small, medium and large thinsg you could do in each of these aspects of life. Say, three things for each box. One must be easy enough to do immediately, one maybe within a week, another could be more ambitious.
Start doing the ones that are easy and add new easy things to the list. Eg - For Health & Fitness: go for a walk, do a 15 minute yoga online session, a 5 minute meditation online etc. More ambitious might be: download C25K and do the first session.
For community service, it could be adding some food to the local food bank or offering to pick up a neighbour's prescription etc. A bigger one could be becoming a volunteer somewhere or fundraising for a charity.
Bit by bit, this technique eases you back into living a productive life. And if one bit of life goes pear shaped, you have 8 other bits that are starting to flourish. It;s a really simple but really effective system to keep you going when you feel really low and worthless.