Passover has two names. The night of deliverance is Pesach. The week that follows is Chag haMatzot — the Feast of Unleavened Bread. Targum Pseudo-Jonathan on Exodus 12:17 preserves the distinction and explains it in a single sentence: "in this same day the Lord will bring out your hosts free from the land of Mizraim; and you shall observe this day in your generations, a statute for ever."
The week is a commemoration of an event, not a continuation of the first night's meal. Pesach the lamb belonged to one night. Matzot the bread belonged to seven days. The two holidays are joined in the calendar but distinct in their purposes. One remembers the deliverance. The other remembers the rushed departure.
Why seven days? The rabbis connected it to the seven days of creation. Seven is the cycle by which God ordered time, and the week of matzot re-enacts a kind of re-creation — Israel becomes a new people, made without leaven, made in a hurry, made by the hand of the Lord. At the end of seven days, Israel emerges reshaped.
The Targum's phrase "a statute for ever" stands in contrast to the one-time commands of the first night. The ready-to-run clothes were for that night alone. The seven days of matzot are forever. Every generation of Israel re-enters the week of unleavened bread and exits the other side with a little less of Egypt inside them.
Takeaway: Passover is two holidays stitched together. The first night frees you. The seven days let the freedom take.