What are the rectangles on either side of the window? Can they be covered?

the rectangle are the windows that OPEN. Past that are speakers in the wall

Get a room darkening/blackout cellular shade. Inside mount is best. Add decorative panels in curtains . Only at the sides.

Forget about "blinds"

This is what I did as I can't sleep in a room that has any light. I ordered darkening shades at Home depot and set them inside the frame. Then I ordered Duette fabric blinds and put them in front of the shades. I pull down the darkening shades at night and then lift them in the day and let the Duettes down. I also added Country Curtain drapes on either side of the windows. Looks super.

It's hard to tell from the photo whether or not your shades can be mounted inside the opening or whether they have to be mounted on the outside, like they currently are. If you can go inside, Hunter Douglas makes the Duette Honeycomb Shades with LightLock which is one of the best blackout products available. It's only offered as inside mount though so if you do outside, you may have to go with a blackout Duette shade and add some side panels to compensate for the light hallow effect on the sides.

How much sill depth do you have will determine if you can go inside bracket or not