A few things help me.
Short commute, so no extra time spent getting to and from the office, and an electric bike that I enjoy commuting on.
Coffee and breakfast at my desk at work, not before going in.
Help at home - husband cleans after supper, and we have a biweekly cleaning lady so I’m not spending all weekend just catching up, can have at least a day to actually relax.
The people I work with are amazing, I like them so much and they like me and each other, it’s a good group.
Taking all my PTO. I do a lot of Fridays off, and usually one solid week off at some point but using them to make short weeks/long weekends feels best to me.
If you really can’t adjust maybe ask about doing the 40 as 4x 10hours not 5x 8?
This does sound like she has depression, and needs to address that before working on the relationship.
If it was not so obvious, I would have said she’s checked out of the relationship, but reading the whole post, I don’t think that’s it, it’s more like she’s just checked out of life in general, so I will hope she gets help and finds her energy and libido and joy again.
Then they can work out a schedule to balance the effort. Some of our “rules” are:
If I cook and you eat, you clean, and vice versa.
We make the bed together.
If the toilet paper runs out replace it!
If the dogs or cats need water, fill it!
Outdoors I do everything (garden, weeding, flowerbeds out front) except mowing and edging, husband does those.
I make all design decisions for the house because I have a better eye, husband makes all vacation plans because he’s good at that.
I’m sure there’s a million ways to set things up to leverage individual strengths and talents and still be balanced enough but none will work without commitment from both people, you do have to want it.