Is there a use for bean juice - the cooking liquid of beans?
It can be used as an egg substitute in various baking applications; search with the keyword "aquafaba" to learn more about this.

Also, it is used as a thickener in some bean-based dishes (eg common in chana masala).

Also, it can be used as stock for some types of soups.

Since you describe the juice as brown, it seems that you are cooking dark coloured beans like black or kidney beans; the same usages apply but might be limited by the unwanted color.

The same usages apply to bean juice from canned beans.

Mind that bean juices do have the same (or even stronger) flatulence-inducing effects that beans have.