I'd combine both sides and make one large room.

put the tv on the large side wall, and position your furniture in that direction.

kind of like they have it positioned here. same premise.

where does the slider go ? is there a barrier outside, between the slider area and the front door? (just wonder if that front door could be moved to the slider)

If not, I'd lose the slider and do a nice french door.

take down the wall w/the pass through if you can, (are you redoing the kitchen at any time? if so, remove that wall now so they can run the flooring under it)

and to further open up that narrow space, remove the drywall from the stairs.

you would basically lower that wall, install any type of railing. (shouldn't be too much since it's small)

do something modern w/the cables if you like.

Like Beth’s idea of tying the two rooms together. Not sure what you’re thinking of for flooring but a wood floor throughout would lighten things up and allow you to use area rugs and furniture placement to define your spaces.
Is this the only area for TV watching?

Agree with Beth re unifying flooring but disagree with suggestion to open stairway. I would do just the opposite- enclose it by bringing drywall to the ceiling. Then fireplace won’t look so awkward and lonely and a seating area or even having dining table there might work.

I would go the route of opening your kitchen and making one open concept to create movement through the space. I would also use the fireplace as a focal point creating it into a a-symmetrical fire place with a sitting bench or nook to the right of it. This is obviously a very simple render, but just to give you a visual on what I am saying. I would love to help you design your space, we offer multiple virtual options!

Here is a “first home” tactic. Take accurate measurements of the whole living/dining/entry/kitchen space and draw it on graph paper. Measure your current furniture and make measured cutouts. Now you can play with the furniture arranging until you find a layout you like.
Yes, definitely redo the flooring in the whole living/dining area with one product. Carpet or hardwood would be my choice. Consider using both sides of the front section for the living room and the fireplace zone for your dining area. Without measurements or seeing your furniture, I can’t guess if it will work.

There are a lot of good ideas here...are any of these ideas possible for you?...if so....do you have a budget?...an idea how long you will live here?....will you be able to recoup your investment in resale?...have you talked to your new neighbors?...perhaps they will share their experience on any improvements really needed...or really worked for them...since you want to start with new flooring i think LVP is the most versatile..economical to install ...and the “wood” patterns easy to keep clean and nice to walk on....