What’s pictured isn’t really practical with the angled ends that don’t even get you close to the table. They’d have done better to leave those off so actual chairs could fit on the ends. A box bay works much better for this than does an angled bay. It’s less expensive to build too.

Are you planning to bump out all 9’?or just 4’ Either is going to require a structural header and siding, foundation, and roofing work in the exterior. With permits and inspections. How deep do you want to bump it? 2’? What size table do you want to fit? Usually the narrow end of the table is what fits in the bump out, and that’s dining seating for one person only. That buys you an aisle width improvement lengthwise. You’d need a 12’-15’ room to be able to fit the long side of the table seating in a bay and have room to get in and out.

Whats the other direction, to the right ? Do you have a measured plan? An indication of the rooflines to judge the impact on the exterior?

If it's a 9 foot long wall and you use a 48" long table then yes you will have room. The angled corners are only there to scoot in to sit on the banquette along the 48" length anyway. Don't be fooled by the idea that you will have a drawer in the built-in cabinetry as shown. Note the height of the seat of the chairs and the height of the top of the banquette cushion - way different. The banquette is way higher. This a a common misconception. Just add the inches up: 4" to 5" h base board, a rail at the top and bottom to hold the drawer in, the top molding edge, the cushion height and then subtract from 18" (the height the top of the cushion should be)...and well you are lucky to have enough for just a tiny niche. I'm 6' and I would not find that banquette height comfy even with my very long legs ; - )

Also prior designer is correct to be aware of the expenses you are walking into. Perhaps you simply remove the door add a window with a built in bench (just deep enough) in front of the wall?I do not see a plan and assume it is not possible or you would have considered it?

Tip: College degreed and subsequent major design office experienced designers always begin by designing in plan ; - )

Thank you! I didn’t want to contact a contractor unless it seemed like a good fit for the space

My daughter"s kitchen is 10 feet wide and has a nice sliding glass door at the end which makes the room seem spacious. She has a 48 inch round table with 4 chairs, but you can squeeze in one more if needed.

Or if you need more seating, you could do a 36 X 78 inch rectangular table with the short side pushed up against the wall on the right and put 3 chairs on each side.

I replaced a window with a box bay window seat. It transformed the room. It’s at the beginning of this post. At the end I added a lot of details about it in answer to a question.

My favorite place to sit now is at the table facing the box bay and watching the wildlife in the back yard.

https://www.houzz.com/discussions/2817830/scrappy25-renovation-part-1-layout-evolution-and-cabinets