I think you have answered your own question. You have done good research, and it shows that "cigarette butts" is more commonly used than the other alternative.
A "butt" is "the part of a finished cigarette that has not been smoked" (Cambridge). Another term for this, but much less common, is "stub".
A "stub" is "the short part of something that is left after the main part has been used, especially a cigarette after it has been smoked ..." (Cambridge). See this Ngram for their usage. The difference in usage between the two is smaller in BrE.
You can, however, write "leftover cigarette butts" depending on the surrounding text. But it is not something you will come across everyday. See this, this, and this.