Yechiel Michel Epstein

“ Even given all these points, this practice, which is limited to the synagogue, is kept for the reasons we have previously stated.
(The 'Magen Avraham' writes that one who forgot to say "You have graced us..." ('Ata Chonantonu') [in the evening prayer] should recite Havdalah first (see there) . It is therefore implicit that he is of the opinion that each individual is usually lighting the Chanukka candles first. The 'Eliya Rabbah' has written so as well, and this is the implication of the words of the 'Gra'. However, the 'Taz' and 'Maharal' from Prague rule to recite Havdalah first. ”

“ Section 1 One should not recite the Havdalah over the Chanukka candles since the blessing of "...Who creates the lights of fire" [one of the three Havdalah blessings] requires one to have some benefit from the light and these candles are forbidden to benefit from. ”

“ This reasoning is also recorded in the Kol Bo in the name of the Raavad of blessed memory. Even though it could be argued that there is no benefit derived from the Menorah there is still the use of fire [before the blessing that recognizes its permit] . ”