Not a pro, but agree that getting the cooktop off the island and under a functional hood will be a nice improvement. Are you open to having the sink on the island? - pros and cons for sure, but good to think about your own preferences.

for seating - I prefer a table to a second island, mainly bc not everyone enjoys sitting at counter height and it takes up so much visible space - it’s also way less flexible. But that’s just one person’s opinion-

If it were me, I would for sure want to address the flooring and get the first floor updated to consistent flooring, like an engineered hardwood

You have 12'8" of width. That limited width plus the patio door and entrance opening to the bathroom/laundry has required compromises that impair function. Like a corner sink, island cooktop/wall oven and limited workzone prep counter space. I'd give up the entrance closet to gain the wall space for kitchen layout by moving the bathroom/laundry access to that location. We don't have a full floor layout to see other closet options.

I'd remove the wall with french doors and the other french door entrance to your living room. Now you have better spacing for a kitchen/dining table and chairs.

Your back view appears to be of a hillside or some other landscaped or plant material suggesting good privacy. I'd replace the patio door and bay with a currently popular wall of windows. Folding at $1k/ft. or wide tall patios at a lesser cost. Island lengthwise without seating Frig and 24" sinkbase and single bowl sink on one leg. 36" induction range Bosch or Electrolux on the back wall with a 48" hood. All wide drawer base cabinets. Micro in the island.

Hallmark and IKEA Vedhamn have European Oak light wood cabinets. DOCA is a Spanish cabinet manufacturer.

Hallmark just announced.

Vedhamn.

Light matte finished European Oak wide plank flooring in different grades from prime to character

is widely available from Hakwood, DuChateau, Monarch Plank, Hurst Hardwood and others. Some are made in Denmark like Hakwood. Most are made in SE Asia.

Can you supply some more dimensions? How long is the ref wall? how far from the left wall is the slider? how big is the slider? how big is the wall between the slider and the bay?

Do you have a dining room or is that table the only place?

Personally I don't mind a cooktop on the island, but definitely not this island! It is not big enough. I also like to have all the tall stuff together, but I think since you have 2 tall pieces, you will probably have them on either end.