@bondo My daughter (our second) didn't sleep through a single night till she was well past 24 months. She's 5 and still probably gets up once a week. It gets better slowly with a poor sleeper. We can get a feel for it and if she hasn't had an exhausting day of playing, we give her half a melatonin gummy, so probably .5mg, a half hour before bed.
The big thing is to get to where you have a sustainable base line. Like even ONE night of sleep is a big deal. Maybe get a hotel room or stay at a friend/relatives or something. My wife was super supportive and probably slept with her 75% of the time or more, but one of us had to sleep in her bed for another 2 years. If she goes to day care, take a day off for a sanity break and to catch up on sleep. As for working out, I just stopped and only got back into it in the last 12 months. I'm probably an old dad but I haven't played vidya since PS3 and I don't miss it. I keep a small woodworking bench with projects ready to go and pick up and put it down as I can. Videogames are an illusion as far as relaxation goes, I built a raspberry pi with 8 and 16 bit games and that helps, the new games just release too much dopamine and it makes the rest of life kind of suck, especially the boring repetitive parts of life, but I have no science to back that up. I did do some hiking with the older kid (carrying him at least half the way most of the time) and that was a great outlet and seeing him see things for the first time was amazing. Kids + Nature really recharge me. Cooking on campfires, tent camping (even with two diaper age kids) is so miserable yet rewarding it makes your house feel less like a prison. As for diet, I'm assuming you're feeding her healthy food? Try to eat what you feed her lol, if they're on the nuggets and noodles plan, then do quick chicken breast in the air fryer with something green. Another killer for me was alcohol. Thousands of empty calories and it kills sleep/metabolism so I have to limit sweet sweet whisky to Friday nights only.
You're at the hardest part, I promise it gets better. Any day now it will turn the corner and you won't even notice it. Just keep your head above water.