You have lots of options with a triple window. You can mount roller shades for black out purposes by mounting them to the top of the window frame on the inside as you probably don't have sides on the middle window. You can do roman shades the same way and get a single valance across all 3 to make it look more united. You can do woven wood blinds the same way. You can also do bottoms up/top down shades like duettes. If you instead choose to mount outside the window frame, you can do drapes on rings or better on a traverse rod that will close and open easily. You could also get vertical gliding blinds or drapes...check out what hunter douglas has to offer. These are more modern and neater than vertical blinds. You could also do a combo, for example woven wood blinds with drapery panels in between to hide the breaks in the blinds, but that will cover more of the window. ...and yes, you can get woven woods and romans lined with black out material.

I would suggest two rods on the right hand widow just big enough for each side window, it looks like you are tight to the far right wall so you don't have room to pull the current curtains back off the window to appreciate the view. because of that I would use a set of sheers only on the right window and the same sheers with the current curtains on the left side, I would also bring all the rods down about two inches from the current height, making sure to line them all up the same. if you have the will, i would then make the tv wall more of an accent with barn wood or a cool wall paper between the two windows.

I would absolutely not hang drapery from curtain panels that high. What you need to decide is what you need to control .... lighting, privacy, or both. If you don't need to cover the top windows due to either of those reasons, then just leave them as is and only focus on the lower windows. You can use window film to control lighting if you need to. But regardless of what you decide to do with window treatments, you need to paint all of the window trim a white color.

Looking at your setup from that second angle suggests you’d have proper clearance on the left but now I wonder about the right side The space on the right is limited by the protruding fireplace “trim” (the mini “hood” above the fireplace opening and the detail below the opening). To see what might work you could purchase a 96” or 104” drapery panel, (whatever appropriate length) hold it up at height rod would be, and see if it hangs ok. Does it look squished, left to right by the fireplace? Does it hang freely? A heavier fabric panel will take up more soace, especially if it’s lined. Maybe a cotton canvas but no lining, or a blackout panel would fit. To help you decide about adequate space, consider the function of the slider. Do you open it a lot? Is that outdoor space a spot you use all the time, or does the door stay primarily closed and youre not going theough that door much. The right panel could hang partially over the door handle (door seldom opened) or it could hang so it fuly clears the door handle (use door all the time). Alternatively, you could mount a shade over the arched window that is long enogh to cover the sliders when shade is let down. (Prob requires a custom made at this length). Whether a shade or drapery, the slider door handle and limited width and height of space will inform your decision as Im sure you already know. Either woud work, but neither are ”perfect”. But perfect is seldom needed. The pros have great advice; maybe they‘ll weigh in