There is such an environment on Earth, called the Twilight Zone or more formally the Mesopelagic Zone. Notably, it is insufficient for photosynthesis. But how dim do you intend? Earth is rather dim according the the residents of Bellerophon or OGLE-TR-56b. Hal Clement was prescient with Iceworld in 1951.
An environment is ruled by available energy. Having far less energy on an absolute scale could be abundant if the chemistry is designed to work at that energy level. Such molecules are fragile by our standards, and the lower temperature is required so as not to smash them apart with random motion and nearby molecules rocketing through it.
Just as the natives of Sarr, breathing sulfer and drinking copper chloride, consider Earth to be impossibly cold and too dim to see well, Nadreck’s kind finds Earth to be inhospitable with blood-boiling temperatures, vast oceans of solvent and highly corrosive atmosphere.
If there are a suitable suite of reactions at the proper energy scale for life to exist using them, then that scale will be normal and comfortable.
If not, then it will be too energy-poor for life to take hold. Where low light is an extreme environment that can be explored by life that finds something else more optimal, then it is seen to be impoverished and harsh for that life.
In your case, the whole world is like that, so, it won’t be colonized by a biosphere that is comfortable somewhere else. It will be comfortable there, if it exists at all.
To get the kind of situation you want, perhaps life evolved and thrived under different conditions; then the conditions changed globally, leaving non-optimal biochemistry to cling to existence.