If your point is that Haman is an Agagite and therefore he's a descendant of Amalek, that supposition is definitely false as Chronicles contradicts it. Nowhere does the book of Esther (Megillah) nor any other book in the Bible define the term Agagite to mean a descendant of Amalek. The idea that Agagite is related to Amalek first appears with Josephus, but it's not of biblical origin. Amalek is long dead.
in Chronicles, the Amalekites were only eliminated in a specific location, not exterminated globally
In Chronicles is says "the remaining Amalekites" were exterminated. Why do you think this means there were more elsewhere?
Saul killed them down to a single man. Later on David had to deal with a bunch more and a few got away. Chronicles says the leftover is now gone too. Also if you compare the last part of Obadiah with this chapter in Chronicles, you'll see by the wording that it's a fulfillment of wiping out the major decedents of Esau. If you read the rest of Chronicles, you'll see the Edomites were wiped out too, meaning no one from Esau is left.
Agagite is a descendent of Agag, full stop.
If you assume the two must be connected, then you'll come to that conclusion.
In the same story just one chapter earlier, Mordechai is termed a יהודי, a Yehudite (Jew), yet it also says he was not a descendant of Yehudah (Judah) but of Benjamin! He was however from the kingdom/area of Yehudah (Judah).
The Hebrew אגגי can mean descendant of Agag, but it can also mean someone who comes from a place called Agag, which was a city in the Median Empire. Similar to what Yehudite (Jew) meant for Mordechai.
But it can also be translated to be a term for someone who is haughty, which fits Haman's character, or it can mean it in a figurative sense that he acted like Agag, or seemingly trying to get revenge for him.
Given that Chronicles chronicles the total destruction of Esau and Amalek's lineage, explaining אגגי to mean an actual descendant of Agag is a real stretch. It's popularly explained that way, but it does not have a leg to stand on. A close examination of the earliest commentators show that a few mention it, but most shy away from it, and remain silent on the matter. It's probably the most popular explanation today because it ties up the story of Saul (from Benjamin) in a nice little bow, or because people want to show the enemy lives on, but that doesn't make it true.
If your point is that Haman is an Agagite and therefore he's a descendant of Amalek, that supposition is definitely false as Chronicles contradicts it. Nowhere does the book of Esther (Megillah) nor any other book in the Bible define the term Agagite to mean a descendant of Amalek. The idea that Agagite is related to Amalek first appears with Josephus, but it's not of biblical origin. Amalek is long dead.
In Chronicles is says "the remaining Amalekites" were exterminated. Why do you think this means there were more elsewhere?
Saul killed them down to a single man. Later on David had to deal with a bunch more and a few got away. Chronicles says the leftover is now gone too. Also if you compare the last part of Obadiah with this chapter in Chronicles, you'll see by the wording that it's a fulfillment of wiping out the major decedents of Esau. If you read the rest of Chronicles, you'll see the Edomites were wiped out too, meaning no one from Esau is left.
If you assume the two must be connected, then you'll come to that conclusion.
In the same story just one chapter earlier, Mordechai is termed a יהודי, a Yehudite (Jew), yet it also says he was not a descendant of Yehudah (Judah) but of Benjamin! He was however from the kingdom/area of Yehudah (Judah).
The Hebrew אגגי can mean descendant of Agag, but it can also mean someone who comes from a place called Agag, which was a city in the Median Empire. Similar to what Yehudite (Jew) meant for Mordechai.
But it can also be translated to be a term for someone who is haughty, which fits Haman's character, or it can mean it in a figurative sense that he acted like Agag, or seemingly trying to get revenge for him.
Given that Chronicles chronicles the total destruction of Esau and Amalek's lineage, explaining אגגי to mean an actual descendant of Agag is a real stretch. It's popularly explained that way, but it does not have a leg to stand on. A close examination of the earliest commentators show that a few mention it, but most shy away from it, and remain silent on the matter. It's probably the most popular explanation today because it ties up the story of Saul (from Benjamin) in a nice little bow, or because people want to show the enemy lives on, but that doesn't make it true.
You can see plenty of other places discusses aspects of this too: https://hermeneutics.stackexchange.com/questions/8193/was-haman-an-agagite https://www.abarim-publications.com/Meaning/Agag.html https://en.wikipedia.org/wiki/Agagite