“The Rambam adds the words בבהילו יצאנו ממצרים before the passage הא לחמא עניא with swiftness did
we leave Mitzraim. What does the Rambam accomplish with this addition? ”
The simple reason is that it is really part of Yachatz (so is the passage הא לחמא עניא see Rishonim Kol Bo etc.) and is a reason why it is called Lechem Oni (based on the verse of Ki Bechifozon…).. see the Hagadah of Rabenu Rav Avrohom Ben HaRambam.