I feel like we actually are not sure about the answer (as there have not been many detections so far, so our knowledge about gravitational waves is probably not very deep), so this might be too speculative as a question. Even a qualitative explanation would help me a lot in this - I'm trying to picture "how the sky would look" for a hypothetical artificial being that can detect gravitational waves.
I'd also like to know the estimated energy density of gravitational waves in the Universe (I tried searching for it, but wasn't very successful in finding the answer quickly, but I might have searched poorly) and if that is relevant in the cosmological context (if that can even be calculated with current data). By the way, my understanding of gravitational waves is very close to 0, so being a bit didactic would be advisable - not saying you can't use equations, but I'd be more comfortable with numerical comparisons.