Does the colour of the eraser matter? Today I saw that erasers can also be of black colour. Would the colour matter in terms of better cleaning/erasing? Can a black eraser perform better that a white one?
According to this article,

because of this eraser’s black color, you can expect your paper to
stay clean and smudge-free, no matter how many times you need to erase
a mark.
The color isn't really what matters, its the quality and type of eraser. Almost all erasers are dyed, so that's the only thing that effects the color. Depending on the materials you're using and types of canvas/paper, different erasers will work better.  So if the black eraser was better quality, then yes, but overall, the color means nothing.