Here is a view from standing in the dining nook area. The island will have L shaped seating on living and dining side.

Kind of late? : )

I have a good sized kitchen and skipped pendants over my island. I have a large triple window and did two pendants at the window. I wanted people to look through the space and not have the eye be stopped by dangling pendants in the middle of the kitchen. I also have lots of recessed lights and under cabinet lights.

Use 4" recessed lights.

I too skipped the pendant over the island and recess lights. The pendant would have been a distraction in my kitchen

The rest of the Kitchen lighting could affect selection of island lighting. Where is it and why not already installed?

Also, having island seating on the other side of the beam (what I understand to be inside the Living Room circulation) is not good for lighting (pendant possibly crowds to beam, or possible shadows depending), nor is it good for the occupants of those stools feeling they are outside the Kitchen.

I’d actually keep the island lighting simple and use the more decorative fixture over the dining area. With the unusual layout, that gives you one clear focal point instead of having pendants compete across different sightlines. A sculptural moon-style pendant could be really beautiful there and add some character without making the island feel busier.

I recently compared several moon-inspired lights, including a pendant design, and showed how they look in different interiors if you’d like some visual ideas: https://youtu.be/g-R98L8EdII