>>725483943
No clue if you're even going to see this but yes, they're Pieces of Eden.
In the base game Nuno Caro outright states this in his discussion with Duarte when you're in the third Animus Ego section talking about how the higher ups in the Order gave him a "small fotune based on their perceived powers" and he doesn't really care about it so much as how much he can profit from Japan.
In Claws of Awaji it's constantly called the "Sword" with a capital S and Yukari herself implies it will grant her so much power she will able to rule Awaji with an iron fist along with take over the rest of Japan.
Keep in mind that Memories has Taka stealing the Sword of Eden from Nobunaga who was going mad because of his lack of Isu blood wielding it. While Memories is now not canon it's likely they still want to act like the Sword is still in the time period.