Not a Pro. Your rushing, if you post a pic of accurate dimensions of the room you will get so many different layouts from the posters on Houzz and one of them will work for you and your needs. I would not make a separate area for the baby and toys in your room, because they out grow the area fast, but I would make sure you have decorative storage to house the little toys, etc. Something that can later be used to store board games, blankets, etc. Think long term. Don't rush, just to fill the room.

Do you have plans for the niches next to the fireplace? Maybe builtin storage cabinets and TV on a pull-out swivel on the right. The L side you could leave blank or have shelves above the lower cabinet. It will add some architectural interest and allow for storage. Then a seating area in front of fireplace - sofa and 1-2 chairs. A small desk area in the space between sofa area and dining. Though I’d probably have a computer station that closes off (do you need for desk top or just lap tops?)

I agree that painting the back wall behind the TV black will help hide the empty space. If I had to place a TV in this space I would probably center it. You are already way over viewing comfort height and a few more inches won't make a big difference. I would also do something to camoflage the TV. I'm not a huge fan of mirrors, but they do have mirrors that you can place over a TV and they look like a mirror when the TV is not on but the TV picture is displayed when the TV is on. Other options include art or doors over the TV. Here are some ideas: https://www.tidbitsandtwine.com/the-great-cover-up-7-ways-to-disguise-your-tv/

I understand why you wanted to have the bistro table/chairs on the window wall between the patio door and the kitchen passageway….it makes sense to have your dining area adjacent to the kitchen. The open wall at the opposite end is the perfect location for the tv. So swap the sofa and loveseat and anchor them and the cocktail table on the rug (front legs of sofa/loveseat on the rug), so the loveseat will pull in closer to the fireplace, leaving room behind for the dining area and access to the patio door. The square end table could then be placed in the corner between the sofa/loveseat.