Question: Why does Al HaNissim not mention the mitzvah to light nerot Chanukah?
Answer: Rav Yehudah Gershuni, z”l, son in law of Rav Eliezer Silver, z”l, discussed this issue. He noted that the Gemara (Shabbat 21b) says that Chazal’s takanah establishing Chanukah was made a year after the victory of the Macabbees. Rashi writes that the takanah was to recite Hallel and Al HaNissim. He writes nothing about lighting Chanukah candles, which seems to imply that it wasn’t part of the original takanah.
Rav Gershuni suggested that as long as the Beit HaMikdash existed, there actually was no obligatory mitzvah to light a menorah in one’s home. (See Kol Tzofayich pp 524-528.) This would explain, of course, why the original takanah did not refer to the obligation to light nerot Chanukah.
I would like to build upon Rav Gershuni’s suggestion. Al HaNissim concludes by noting that “your sons came and lit candles in the courtyards of your sanctuary.” Note the terminology. The tefillah does not say that Chazal imposed a takanah on klal Yisrael. It states, rather, that klal Yisrael by themselves assumed the practice of lighting nerot Chanukah. (“Nahagu ha’am” rather than “hitkinu.”)
Lighting Chanukah candles became a national mitzvah because klal Yisrael adopted the practice (although it’s possible that a later beit din may also have ordained it as an obligatory mitzvah).