Is this actually intended to be a dinning room? I’ve never seen a closet in the dining room. Maybe just remove the closet and bar and open the space up. Or if you need more closet just make it a closet.

Depends on the look you want. Do you want a built in look, or an open feel? Do you want to just put in a piece without having to do any work or have it built? I don't really think you have the space for an actual bar (or island) to stand behind, so I think a bar cart or maybe a cabinet so that the items are hidden most of the time would be what is called for here. Depending on your DIY skills, you could build in a cabinet with shelves or an upper cabinet. Not all these examples will be your style, but I think you can get the idea. You can even retrofit an old dresser, china cabinet, hutch, or secretary desk. This one would take some DIY skills or hire someone..... Just a cart....

Because this isn't a separate table but an extension of the kitchen counter I think a chandelier is too large. Even a pendant is going to look strange in isolation. So I would just plan your recessed lights accordingly. I have a small island and I don't have pendants over it - and I don't miss them. I didn't design my kitchen but when it comes time to remodel I won't be adding any. Sometimes less is better. Get your hood installed and choose an attractive backsplash. If you're interested in beachy then how about blue or green glass? Once you do that I don't think you'll feel the need for more bling. Also, the fixtures you're interested in are the same color as your cabinets so it would blend in anyway. You should think about adding some contrast.

for sure, i would just make sure you like the counters and floors together - we view counters vertically when shopping for them but they will be large horizontal surfaces in the room once installed so floors & counters really play off one another — if you love the green walls then leave them - Your darker walls and white ceilings are high contrast so the eye picks the many jigs and jags in the ceiling & soffits, which you may really like - i was just saying if it were me, i would want to downplay that and paint everything a soft white but it’s just personal preference