Reward for Observing the Lighting of Hanukkah Candles

Shalom,In the Mishnah Berurah (Siman 671, Halacha 1), the tzaddik brings the reason for Maran’s ruling. Is the reason because the Gemara says “One who is careful with the mitzvah of lighting candles will merit sons who are talmidei chachamim,” as it says “Ki ner mitzvah…” — and Rashi explains that “ner mitzvah” also refers to the Chanukah light? So is that the real connection, that since Rashi tells us the “ner mitzvah” includes the Chanukah candle, that’s why it’s mentioned here?Or is it more correct to say that the reason is simply because the Gemara itself says “ha’ragil b’ner…”, and Rashi is just clarifying that the ner mitzvah mentioned there refers also to the Chanukah light?As the Rav sees, in the first version I included the pasuk, and in the second I didn’t. Since the pasuk doesn’t change the meaning much, I just wanted to know which way is more accurate.

Shalom uVracha,

I didn’t fully understand the two sides you’re distinguishing between.

Practically speaking, the Mishnah Berurah brings the pasuk as the source that there’s reward for one who is careful with the mitzvah of lighting the Chanukah candles.