Pouring concrete countertops over lazy susan
You don't wish to retain the lazy susan/turntable?

Then it's fairly simple to turn that into storage space, some of which will be difficult to access (which is why people often accept the LS/T losses of potential space.)

If there's no side next to the stove, you'll need to make one. If there is, you just need to make some shelves, and screw supports for those shelves into the cabinet sides and the wall studs.

You can either paint the drywall or overlay it with plywood depending how much you care what the inside of the "cabinet" looks like.

As for supporting the concrete top, there's two stages to that - if you are pouring it in place, that's the tricky time and you need to provide adequate support (temporarily) to keep the heavy wet concrete from sagging on whatever you use as a bottom form, as well as enough reinforcing that it will support itself when cured. If you are pouring and curing it separately, then installing it, you only need to hold it up when cured, and that can be more cleats (robust ones) on the walls, and perhaps a diagonal brace across the corner.