On front seat, if it truly does not come off while pushing release on one side and using some force, then i'd perform a mild surgery.
Open up backrest from rear, push the notch on headrest holder without release thingy and while pressing it on other side, pull out until it can be rotated 90 degrees. Then headrest should be removable and holder can be inserted back. Can be done in car.
Copied pictures from my seat cleaning:
https://www.a2oc.net/community/inde...ing-in-washing-machine-cloth-with-pics.46722/
First start by pulling out "whatever it's named, so lets call it a large clip" near bottom of backrest. Tools are just for holding it still for picture to show twist. Small screwdriver etc may be used to get one end out, and then pull by hand. Additional small ones on both ends.
Same thing with sides and then lift it:
If you lift cover, you can see small notches to press with screwdriver etc and headrest thingy-s will slide out (one already removed).
And if it not enough access to push notch, 2 circlets need to be removed:
Near top we can see metal wires bended into circle. Objective is to bend them sideways enough that they can be removed, they will be reused. Turn them out and remove long wire hiding inside if needed:
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Second option might be popping off cover to see if wire can be pushed away with some sharp tool, but it's not easy probably and might damage it. Picture just to show wire in right one: