I have a day job so I don't have a lot of these problems people report about not knowing what to do with their time during fasting. I have to go to work, attend meetings, write, and even travel on business during fasts. There is simply no way I can lie around in bed all day doing nothing, nor would I fast that way even if I didn't work.
During the weekends on fasting, I try to avoid going out too much. Mostly to avoid food situations, like parties or restaurants. I've done it during work, but on the weekends I avoid it.
I tend to do a lot of cleaning and purging when I'm fasting. I clean closets, drawers, and cabinets, clean all those places that get neglected throughout the year, like behind the stove and fridge, the top shelves of closets, whatever. I call Goodwill and have them come get all the crap I've purged from closets and drawers.
I live in a metro area so I have to walk for transportation much of the time. I would avoid running during fasting, though. I also love to read so no problem there, I read more and go to the library more. I also like going through museums when I'm fasting, which is really "strolling" and not walking.
Read Marie Kondo's book on organizing and minimalist living. Get rid of everything in your house that doesn't bring you joy. It's also a
good time to catch up on any revolutionary reading. I re-read Kapital, re-read Lenin, listen to Fidel's speeches, read Kim Jong-un's and Stalin's speeches, etc.
To me, a lot of feeling "out of sorts" during fasting has more to do with the habit of eating and rituals around food. We spend an inordinate amount of time in our lives getting food, cleaning it, preparing it, eating it, and cleaning up after it. When that ritual goes away, people at some level feel adrift. It's a large part of our lives and the time we spend on it is huge, even psychic time, thinking about food, so you have to find substitutes for it.
Everybody has stress, it's part of being alive. Granted it has chemical and physiologic impacts on the body, but we know physical activity mitigates it, so get moving. I second walking 20 minutes a day. Do yoga or Pilates, or just some athletic body stretches. No marathons. Walk for transportation if you're in a walkable city. Clean and organize your home, that generally takes some bending, lifting, and moving around - activities I consider light toning. Just be careful getting up so you don't experience orthostatic hypotension.
Start reading about low fat plant based diets if you don't know about them. If you want to maximize your body's defenses against stress, once you start eating again you need to avoid animal products and oils.