The wood could be painted.

Stained wood needs to be stripped first if you would like a lighter stain.

Maybe you could clad the beams? Stripping and then sanding (stripping only removed the poly sanding is what removes the stain) is quite a feat for beams in place. Not seeing you finding anyone interested in that mess.

I think painting the walls a light-reflecting white will be easier, and possibly adding skylights.

If you have pictures, that would be helpful to give us an idea of the architectural design and general aesthetic of the home, but without those context clues, we can provide some ideas and inspiration. If you want to keep the wood look of the beams, you can hire or stain them to the color you like, but you can also wrap them with wood in the color/stain you want. Here are some wood beams from our projects in a medium to light color:

If, for some reason, you can’t stain or change the color of the beams, you could lighten the space with a lighter color on the walls, like in this project: