The paragraph we say on burning the chametz is in Aramaic. What is the reason for that part being in Aramaic, but not most of the Haggada? (The search is part of the prescribed Pesach ritual, as is the Haggada.) Was that part added to the Pesach ritual after the Hagadda was written?
The Magen Avraham (Orach Chaim 434:2) writes, that the reason why we say it in Aramaic, is because that was the language that all Jews understood back then, and in order to nullify the Chametz, one must understand what he is saying.
There is another reason, (brought down in Seder Hayom on Biur Chametz) that being that when one destroys food - especially bread - it can cause him to become poor, we say it in a language that the accusing angels won’t understand
I believe that it has to do with how it was added later on to the Haggadah. Let me explain:
There are 3 opinions as to who wrote the Haggadah: 1) In sefer Zechariah Lechaim 4a he mentions that the Haggadah was compiled by Rebbi Akiva and his source is the Yerushalmi Shekalim 5:1. 2) In Sidur HaRashban 29a he writes that Rebbi Elazar ben Hurkanus compiled the Haggadah. 3) Finally in the book Kol Hamevaser Pesach 3 Ot 12 writes that Eliyahu Hanavi compiled it and it was revealed to the sages. Whichever opinion we follow, it was in the times of the Tanaaim and earlier which means they spoke Mishnaic Hebrew (the hebrew/lashon of the Mishnah).
The paragraph we say for Bedikat Chametz is found in a few places: In Mishnaic Hebrew: 1) Yerushalmi Pesachim 2:2, Rambam Hilchot Chametz Umatazah 3:7. However if you look in: Sheiltot Derav Achai Goan Siman 74, Rif, Rosh on Pesachim 6b, Sidur Rashi page 173, Machzor Vitri page 294, and others, it appears in Aramaic.
Therefore I think that even though we had the paragraph of Bedikat Chametz from the Yerushalmi in Hebrew, the reason its in Aramaic is because the Geonim and Rishonim say that many words needed to be included or changed from the Hebrew text into Aramaic, because its meaning only comes out in Aramaic (just like one can’t precisely translate some words or any words from one language to another). There are many examples of this. For example, when we say חמירא it includes all חמץ and all שאור unlike the word חמץ, and thus even if we were to say כל חמץ ושאור וכו, it wouldn't be as clear and concise (and this would also apply with other examples I didn't mention).