What does the designer of the house suggest?

haha designer? That would be DIY me.

Floor plan of the whole floor? What do the ceilings look like?

What is the intention for the separation? You don't like sitting next the front door when dining? Don't want to see the kitchen mess? Want a psychological shift from the day when you dine? Someone works or does homework at the table and needs less distraction from around?

Well at first I was thinking of separation from dining and living room, but now I'm thinking some separation from the entrance and the dining table would be best. Across from the table (you see just the tip of it) is a galley kitchen.

I'm not an A fan even with the Wonderful build. 10'ceilings down in smaller areas for a relaxed closer contact feeling. The steep roof instead at 6/12 would cover more useful sqft. than the high volume you end up with. You're the designer. Keep giving it thoughtful development. 'A's were meant for very small square footage cabins, imo.

Just a follow up, I've spent countless hours and thousands (and for course will spend thousands more) on our house for our family. There are pouring foundation as I speak. Please don't share with me your dislike of A-frames or why it's a bad idea. I mean seriously.

Here are some ideas: https://www.thisoldhouse.com/living-rooms/21334671/room-divider-ideas

Do you want a sight-blocking separation? I'm thinking that a change in flooring/rug or a flat ceiling in the dining room will define it.

Or, what about a sliding panel?

I thought about a sliding panel. I could do that besides the entryway. The sloped wall on the side facing the living area would prevent this.

So you're stuck, so you think, with this design because of money. To solve your problem how about a rectangular skylight with a hanging live wall. Two sided with a recirculating water feature built in. The water can be very limited and doesn't have to reach the floor. Same with the plant wall. You may need timed led plant lighting. Power from the ceiling. You can diy this.