It would be good idea except I would make it taller. You really don't want to be able to see into the bathroom from the dining area. Here's a screen wall that could be built to still allow light but screens it visually.

No walls. They will be cumbersome and cut the rooms off in my opinion. Good luck deciding! Looks like a wonderful home!

Except for the powder room location.

You could correct the powder room situation by moving it to the location of the walk in closet for the play room. Then make the closet in the play room just 3' deep. There would be a hall behind the closet to enter the powder room. Its very unappetizing to see the toilet from the dining area and I would never use it when the dining area is being used.

Our set up is similar. You can provide division without a wall. We have a support column plus column bump-outs (don't know what else to call them) on the walls at each end or the room. Also have a long runner down the hall portion.

One more consideration about the bathroom. If you make the closet smaller and add a shower to the bath, the room can be considered a bedroom when you go to market the house in the future.