Does it have heat, I see a space heater I think. It looks like the wall with the tv was maybe an exterior wall so it is probably structural so you should budget for that.
I have a much smaller version of your two rooms and instead of opening it up I added doors to sometimes close it off but they are usually open. I decorated the two spaces to coordinate and put a different shape but same color sofa infront of the wall af Windows looking into my tv room but with kids mess often in the sun room I like to close it off sometimes. It also gives me a place to read while my kids watch annoying Disney shows in the living room.
The doors look like pocket doors but are only 1920 doors hung on barn door hardware. The doors also let me close the cats out of the Christmas tree room when I am not watching them
I did not have the budget to open up for it is an exterior wall.
Q