As I believe 'alphabet' refers specifically to the Latin a - z.
Your belief is wrong.
The alphabet, just by its name, is related to ancient semitic origins, the traces of which remains in Hebrew, for example, the first two letters of the Hebrew alphabet is Aleph & Beth, and so, alphabet. But it's origin goes even further back to Proto-Canaanite, also known as the Phoenician alphabet and influenced the alphabets of Arabic, Cyrillic, Greek, Hebrew & Latin.
Further, the term - alphabet - in it's modern meaning means simply all the basic written symbols - known as letters or graphemes - used in a language that uses these symbols to represent a phoneme.
Thus the collective name for a collection of alphabets is 'alphabets' - like I have already used in this sentence.
if I had a list containing 'Latin, Kanji, Cyrillic', what would that list be called?
Whilst both Latin and Cyrillic use alphabets, Kanji is logographic; hence to refer to the list above, one would say, alphabets and logographies.
All writing systems come under alphabets, syllabaries, logographies and ideograms. Some used mixed systems like the Japanese where they have both a syllabary and a logography; in Chinese, they use a fusion of a syllabary and a logography and ancient Egyptian heiroglyphic is ideogrammatic. There is no one word to cover them all.
If you wish to use a term that covers all of them, its best to use an invented term for this. For example, alis, which is an acronym of alphabet, logogram, ideogram and syllabary. The other option is to choose one of these to represent all of them. Semantically speaking the best one to choose is ideograms since all 'letters' originated from such.