LW, I am usually 100% sympathetic to people with spouses who have unreasonable standards of housework and refuse to compromise. But your wife has compromised! She's spending her own money on a cleaner!
If you can't handle the idea of having a cleaner in your space, designate a room in the house as your personal space. The cleaner can't go there, and your wife doesn't have to go in there if she doesn't want to, and you are responsible for all housework in that room. You can even call it a "man cave" if you really must, but "private office" is much less cringey. Anything you're worried about the cleaner finding or breaking can go in there, and put a lock on the door. When the maid is there, you are either out of the house or in your room with the door locked.
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If you can't handle the idea of having a cleaner in your space, designate a room in the house as your personal space. The cleaner can't go there, and your wife doesn't have to go in there if she doesn't want to, and you are responsible for all housework in that room. You can even call it a "man cave" if you really must, but "private office" is much less cringey. Anything you're worried about the cleaner finding or breaking can go in there, and put a lock on the door. When the maid is there, you are either out of the house or in your room with the door locked.