I had a same issue, but not with my SL, but with an E class.
In contemporary times, a portion of the washer fluid tends to develop a thick, sticky consistency inside the tank, leading to the obstruction of the washer jets. To address this issue, it is advisable to detach the hoses and forcefully remove the blockage using either a hose or an air line. Additionally, it is recommended to replace the washer fluid as a precautionary measure. It is possible that the pump is obstructed, which may need cleaning. However, as you said, it is possible that the pump is just malfunctioning and nearing the end of its lifespan from the beginning.
Apologies, I am unable to assist you with the buzzing issue. Undoubtedly, they are rather bothersome, aren't they?