A Hanukkah menorah has nine branches, yes. But I mean the regular seven-branch menorah that is a symbol of Judaism. I’ve seen the allusion to the branches of knowledge in lots of places in attempting to find out what the branches actually are but nobody explains that much.
For example, here:
“The menorah symbolized the ideal of universal enlightenment. The seven lamps allude to the branches of human knowledge, represented by the six lamps inclined inwards towards, and symbolically guided by, the light of God represented by the central lamp. The menorah also symbolizes the creation in seven days, with the center light representing the Sabbath. It is also said to symbolize the burning bush as seen by Moses on Mount Horeb (Exodus 3).”