I suggest you move your stuff into the space, photo it and come back for input based on your own reality. Lots of potential, but practical advice is better when based on what you have or don't have for the space.

Many thanks for the suggestion, I am intrigued by the Arco lamp. May I ask what size your room is, and also does that lamp rotate up or does it only project light down? I like the idea that I don't need to drill any holes in the walls or ceiling.

I agree that the tripod style floor lamps take up a lot of real estate. Many people use a floor lamp when they don’t have enough room for an end table. Why take up the same space with a lamp?

You are paying for the view, so I wouldn’t turn my back to it.

You have a TV, they did not. Due to cords etc. IMHO your only option is the set up as stated with the TV where the round mirror is. Which side of the room you put the TV is a horse a piece. As you said you have similar pieces but why spend an second on their floor lamp...It is a conversation piece, a statement THEY made. Don't give it a thought. Did they remove the window treatment to maximize the "value" of the view? Realtors ploy..will you need something to deal with sun coming in, privacy? I would suggest a pattern with RED--that room really needs color!!!

Agree with not blocking the view- it’s great! The current configuration is perfect and the TV can go, as mentioned, where the mirror is. Once you put your actual furniture in, you will see how a lamp would ideally fit. In the best case scenario, every seating area should have a place to put down a drink and ample light.
I’m assuming this is a rental as you say apartment. Is that correct? If so, custom window treatments are expensive so obviously price should be a factor. If the door is a standard size, you should be able to put 2 panels there for privacy and light control.

Just looked at the picture again. My bad, those are large windows with a standard door. Still think curtains would be your best and least expensive option.