What does the person that designed the house advise?

If you were to put that there it would be visible from the front door. To me it doesn't seem like the best thing to have there, and the space is more cramped than what is shown in your inspiration pics. When designing a house you need to be thinking about sightlines. But if I were you I would bring this up to the architect because it sounds like it is a wishlist item, even if you didn't think about it earlier. However, keep in mind sometimes we can't fit all of our good ideas into one house.

You've circled a stretch that's about 30" wide, and are comparing it to an inspiration photo with a built-in bench that's probably 8' wide!

If you've got chairs at the island and a dining table elsewhere, don't try to retrofit more.

You didn't ask this, but I noticed your plan has dimensions down to a half inch or even quarter inch in some areas. Are they OK with these plans and building to such specific dimensions, or do they prefer whole inches? I think your bay window idea could work if you move the double doors down a bit away from it.

What furniture are you putting in that room? i certainly can’t see that you have room for a table in that space. try putting furniture to scale in there. also you have island seating so do you really need big table, little table, and island?

I think you might appreciate having a table in the living space, for games or to eat while watching a game (or the Olympics!). A bay would be nice just to give a little scootching room, but it won’t accommodate a table or chair, and it will look a little odd there, and the cased opening makes it even smaller. And the table and chairs will block the passage from kitchen to living room.

How many people are you? Will you normally eat casual meals at the island?

Regarding the front door view, here’s a funny thing. My kitchen table is in front of a front-facing kitchen window, and I like it. But, in the living room, ”my” chair is right in front of the foyer and front door, a single with sidelights, and it kind of bothers me at night. Will your front entry have glass?

I'm not sure you have a true concept of size.

A bay in that location, which would really not be architecturally appropriate, would only be about 60" wide once the walls and windows are built. Really too small compared to the 8-10 ft bays you have posted.

I find most bays are not great for eating space and honestly the style of your home needs to be considered plust the added expense of any jut outs on the exterior. If this is where Mark shows it very odd place for this IMO it looks like it is not in the kitchen at all so whay?A 5' table needs min 2' all the way around and in the bay you will need an awkward bench seat so that bay will need to be huge . Get an island use some stools and IMO forget the bay.

You cannot even fit a 5’ table in that design. A tiny 2 top bistro table, maybe. This is more of a tiny home than a family home. You don’t have room for half the things you think you do without a full redesign.

"where Mark shows it very odd place"

Yup, but not knowing all the facts I thought I would make a suggestion that makes others think outside the box. Not sure if my suggestion is as odd as the double doors swinging out on the other side of the house.The person that designed the house knows more than anyone here, so that is why I asked the previous (unanswered) question. Having the breakfast nook a short distance from the kitchen may open up opportunity for multiple uses of the space beyond breakfast, but we do not know the needs of the OP. I assume the island in the kitchen has space for seating.