So I would absolutely keep the rug. I would do a cooler color on the wall like a gray green or gray blue. Get a runner to go between the doors that coordinates with your existing rug. I would add real baseboards but if you can’t just paint a 4” wide white band above what you have to fake it. Add a narrow console table with an open decorative front to hide the air conditioner. Paint the door to the house charcoal gray. I found these curtain panels that to me could mimic artwork to hide the vertical blinds. Then add a seating are there. Keep the bench and mirror as is. I don’t have photoshop so excuse my poor mockups lol.

COATS: I see on the floor plan that there is a closet in the office(?) If so, you could put a door in from the living room/dining room side and have that be your coat closet. Then you could get a shoe cabinet like this one https://www.ikea.com/us/en/p/hemnes-shoe-cabinet-with-2-compartments-dark-gray-stained-20381763/ from IKEA to have by the front door. Otherwise I’d look at getting a hall tree/cabinet like the previous poster mentioned. Floor plan: see pics. If it works to put the door in for coats then put the dining hutch on the wall opposite the dining table. And possibly a couple of display cabinets to go behind the table. If not, put the hutch behind the table and put the hall tree wall opposite the dining table. Recessed lights: I laughed that you laughed about recessed lighting. They are extremely common in US no matter what the style. I love the ones you found and would definitely go in that direction. Floor: Love the floor. Would have area rugs to define living and dining or at least the living space. Bay Window: would need to see a picture. I think there may be some other options. I would be nice to be able to accentuate it. (See pic) Interior Design: I like where you are headed. Crown Molding: YES. Just do a little research on how wide. You don’t want to skimp. It will make your ceiling feel taller. I would paint it white like the baseboards.

Is this a new home? Whoever did the tile work did a shoddy job. Door to left in the entry...what's going on there? I see tile from another room. Before you invest in furniture, think about a rug. It will disguise mistakes and warm up the space. Depending on the style you choose, it will also give you inspiration on how what else you want in the area. Consider two rugs and rather than a mirror add some wood into the mix.

Wow, that looks so nice. Thank you for your advice!