How long will it take before you have the apartment unpacked and the house sold? If unpacking is that much work, could you pare back the amount of stuff you have?
Houses in a lot of areas are selling as is for over asking price right now. Are you sure you really need to do much to get the house ready to sell?
If this is something that's going to go on much longer you should see a doctor or a therapist. I know that's just one more thing to do, but what you're describing is a medical problem.
Best case a few weeks, worst case who knows. I'm hoping for a fast sale, given how the market is right now, but our house has some unusual challenges (missing walls and even floors in some rooms, roof leak, dry rot, damaged retaining wall, etc) that make it likely not to be an easy sale. The only preparation we're still doing is getting some junk and trash out to the dump, to prepare for the photographer. The realtor wanted me to hire a cleaner, but that felt like massive overkill for a house with exposed floor joists.
Can you take a short leave from work?
Can you temporarily hire out cooking and cleaning?
Can you recruit or hire help to unpack?
I've done some pretty radical things to get through a lot of insane burnout situations. None of what you do needs to be sustainable, just enough to get you through whatever it is you are going through.
My point is that the approach is the same as work burnout. You have to figure out what it is that you need most.
How would you handle it if you physically couldn't manage everything you are trying to do? What would you adjust?
I'm a long-term contractor (not independent contractor, I work through a contract agency), paid hourly, and I don't have short term disability insurance, so even if I got cleared by a doctor to take leave, it would be unpaid, and unless I could get it through FMLA, I probably wouldn't have a job when I got back. Which, since work is currently the least stressful part of my day, doesn't seem reasonable. And that's assuming I could get a doctor to sign off on it, which is not a given since I don't have any physical symptoms (yet, I know.) Also, while my boss has been very understanding about people deprioritizing work over the last year+, he is starting to get impatient to have us back in the office. Since this is easily the best job I've ever had, as far as boss, work-life balance, coworkers, and the job itself, I'm not eager to lose it.
Honestly, finding someone to hire for cooking and cleaning and then managing them sounds like more effort than just doing it myself. I did get a lot of help from my family during and after the move, including a lot of unpacking, but we've reached the stage where everything we pull out of a box requires
decisions. Where does it go? Do we have space? Can it go in storage? Should we get rid of it? That's just exhausting, and not something other people can help with. Plus most of our network lives over an hour away, so I can't just ask them to run errands or come by for an hour.
What would I do if I had a physical ailment instead? That's a good exercise to try. I tried writing out a few scenarios with different types of injuries/illnesses, but all of them basically boiled down to further damaging DH, overtaxing and damaging our safety net (friends and family), possibly losing my job, and making our lives permanently worse. At least with a physical injury, it's harder to deny FMLA. Maybe that's just my pessimism-brain talking? Or just the US healthcare system at work.
The fact that DH is even further into burnout than I am (though I don't know if he's acknowledged his symptoms being related) complicates things. At least I'm not (yet, I know) having the physical symptoms of memory loss, poor sleep, headaches, and muscle aches. Even before we started planning the move, we'd talked about trying to get him some leave, but his department is so small it's hard to get approved. I don't dare do anything that's going to add to his load, and he has a lot of financial anxiety.
The more I write out, the more it feels like I just have to manage to tread water for another 3-4-ish weeks until we can get the house sold, and hope for the best. Anything I try to change right now risks making something worse.