Do you have a question?

Is the wall opposite of the closet door still inside your kitchen?? If you want to use it for kitchen overflow - it would be better if it was was part of the kitchen area.

Your photos show very different uses of the space. The first photo and last photo show coffee bars/stations (only the top one has a sink). I wouldn't do something like the fourth photo unless you have a need for shelves to display specific items that you already own - in other words, don't make a ton of open storage if you then will need to go shopping to find items to display on all of those shelves.

If you add some photos of the the closet area/the inside of the closet/the other side of the closet + what you really want the primary used to be, we can be more helpful.

" Currently I have a closet that opens up from the kitchen that is under our stairs. "

Context is key. Post up pics of your area in question.

Current situation. I'll be updating my kitchen and floors and want to see about possibly taking down this wall

What wall are you thinking of taking down?