Have you tried CBT? Because a lot of the comments you are making, which underpin your unhappiness I can now recognise as disordered thinking. CBT really helped me to understand that I had deeply ingrained disordered (or distorted? - I forget the term) thought patterns. And by spotting them, identifying what type they were and replacing them with more neutral, unbiased or compassionate thoughts, I was able to make some really positive changes.
One example you use and I used to use similar thought patterns a lot:
"Everyone else seems to hold things more lightly, and they seem to find life easier. I don’t."
First, literally everyone else does not hold things more lightly. Some people do (maybe they lack depth or sensitivity to the suffering of others around them?), others do some of the time but not always, others don't - they see life as bleaker than you do, and create havoc and despair. It's a sweeping generalisation that creates a sense of your own inadequacy but it's false.
Second, when we compare the one of us to the rest of the world, we are always lacking. We cherry pick one person's smily family that love being together, another person's immaculate home, a third person's high income and ask ourselves: why am I not wealthy, immaculate and loving family life like everyone else. If you dig down, you often find they do that one thing well and struggle with others. That's just human. It really helps to stop comparing the one of you or your one family to the entire rest of the world and cherry-picking the best bits from all over to compare with your own.
Next, I think it is healthy that you are quite clear on some reasons for your unhappiness and possible solutions. You do nothing for yourself. Of course that is not good. Can you work out a way to do one or two things that you'd enjoy every week? Ring fence that time?
If it's not possible (and I know there are periods in life, eg if you are a single parent with SEN DC when life is so hard and money so tight, you can't just sign up for dance or art classes or whatever) then the key is to wedge tiny, easy splinters of joy into everyday life. That's what I did.
Examples:
First thing in the morning, put on some beautiful piano music.
Chuck some bread out for the birds, brew a tea or coffee and watch them feed while the music floats over you for five minutes.
At night, while prepping dinner, put on your favourite upbeat music from your teens or your youth - or bands you have heard recently. The cheerful or beautiful stuff. Turn it up quite loud while you are chopping veg.
Once or twice a week, cook your own favourite food. If DC don't like it, they can have beans on toast or tinned spaghetti with grated cheese and peas.
Before bed read a page or two of gorgeous poetry or of a funny escapist novel.
Watch reruns of shows that make you laugh or films that are uplifting. Sign up for good news websites that focus on wonderful medical breakthroughs, compassionate aid, acts of bravery and kindness. The usual news is driven by awful stories. But there are wonderful stories out there, getting no attention.
Another thing that can open life up is: do something new every day and keep a brief record of it. Just trying new scents of bath foam or a new type of tea, or walking a new route to or from work, spending 5 minutes in an antique shop etc can start to open the mind.
Counterbalance the sadness. you are right that it is awful there are beggars, and life is hard. But it is also true that life can be spectacularly beautiful and kind. Look for three examples of such moments every day. When I actively did this I saw wonderful things. One that stays in my memory is: A train pulled into Clapham Junction. Our guard got off to check the platform and blow her whistle. A platform officer just held out his hands, pulled her into a shaft of sunlight, waltzed with her for thirty seconds then she got back on the train and we set off again. But there are ordinary ones: young men offering seats to older people on the tube, or offering to help strangers with suitcases and prams. supermarkets handing out free flowers and chocolates on sell by dates, rather than having them go to waste, buskers playing stunning music, gorgeous street art, beautiful skies, blossom in spring, sunrises and sunsets etc. Allow yourself to appreciate these endless examples of kindness and beauty in life to offset the darkness.
Sorry for this massive essay. But I have struggled in the past and these things all helped me. I hope some of them work for you too.