You want 12" overhanging the wall, minimum, 15" preferable. I'm cutting down a lot of bars so you may want to make the wall flush with your cabinet tops.

Part of a wall requires just as much of a extended header as removing the whole wall. Has your contractor discussed those structural implications with you?

Are you going to have 2 eating areas next to each other?

Is this just going to be a pony wall or is there going to be cabinets against it?

Not familiar with the term ‘pony wall’. There’s no cabinets above or below the wall. I just wanted to open the area up a bit to make it brighter in the dining room. The quartz counter will be as a ledge/pass through.
There will be a small table for 2-4 in the kitchen area, which is for 90% of the time and the dining room for larger dinners of 15-20.

So, basically a half wall in between the two eating areas with a 12” piece of stone on top....?

I’m sorry but that just seems awkward. I can’t picture it at all. Can you draw is a floor plan/ diagram?

Too goofy for words. Separate formal and casual eating areas need to actually remain separate. If you have a lighting issue, you fix it by addressing the lighting plan. Not by doing structural alterations that cost you thousands and thousands to actually accomplish correctly.

Start by putting in some lamps.

I would not recommend your plan as a good design solution.