The title of your post is treatments for the windows but it sounds like you also want something over the sliders? Do you need privacy? How often is that door used? Just looking at the overall space if you want curtains for all of the openings I’d do one long rod and make it look like 3 panels when open. But Im not sure curtains are the best option here. Why do you want curtains?

You really have three different windows to dress. Have you considered roman shades for the two smaller? Use identical fabric but different applications. For the slider I would have the panels open only to the right so you could have one half of the window/door covered no matter if it is open or closed and then stack would never get in the way of the opening. I can see how one long rod would work just fine here. You will need supports a few places through the middle

This room is a converted porch which faces East and gets so hot in the Texas summer. I was thinking blackout curtains or highly UV filtering on both door and windows to use when needed. It would be nice to close off the light for daytime movies also.