One to cover both.

I can see baseboard heaters in your photo. If electric, a panel drape could be a fire hazard.

You cannot add drapes because of the baseboards. If you need room darkening and light filtering, I recommend replacing your blinds with something like this.

https://www.hunterdouglas.com/window-treatments/sheers-shadings/silhouette

I'm guessing the baseboards are radiant heat and there are no issues with drapery panels.

If those are hot water rads there is no issue with drapes there but I would do probably a bit more semisheer fabric for the drapes and run them all across that wall for a much more polished look.

One rod.

Due to the size and style of the room, I’d do one rod for a simpler look.

One continuous drapery rod will work great!