Easiest solution is to frame it in and drywall it.

drywall the top portion then depending on how you plan to use the space, i would remove that light fixture. looks like you have space for the table in the kitchen. you can use the electrical to run rail light or cans.

here are some ideas.

Drywall it in from the living side. Maybe install a secret hatch from the kitchen ceiling for extra long term storage? Or get a contractor in to see if it would be cost effective to just eliminate the false ceiling in the kitchen.

in this case you will need to hire somebody professional in this kind of stuff, I don't think it is possible to do it by yourself

Put a low table against it....it's fine. I would definitely change out that kitchen floor! and modernize the cabinets because you can see into that room!

I like your cabinets! That is not a load bearing wall as the back darker one is probably. With the cabinets there you will always have this look. You could do a wider counter top to be more useable. And add tile around the floor to match your kitchen.

Ken