What was the significance of Pomegranates on the Kohen Gadol's "Me'il"?
Why specifically Pomegranates and not any other shape?
Welcome, and great question!
This is one of the many questions that Ramban (Shemot 28:31) asks on Rashi (and others), and he therefore rejects their opinion.
However, in responding to Ramban, Mizrachi (28:33) asks right back - what's wrong with pomegranates? If it had said another fruit, you would have asked the same question:
ואיני רואה מקום לאלה הטענות כלל כי מה שטען למה היו עשויים כרמונים ולא כמין תפוחים לא ידעתי למה בחר התפוחים יותר מן הרמונים
And I don't see a place for any of these issues at all. That which he asked "why were they made in the form of a pomegranate, and not in the form of an apple?" - I don't understand why he would choose apples any more than pomegranates! (my loose translation)
Various online resources offer the symbolism of the pomegranate (although I don't see much in the classic commentaries).
Rabbi Moshe Alshich (cited here), based on the Talmud in Zevachim (88b), understands that the pomegranates represent silence, and they therefore surround the bells, which make noise, to show us that there should be silence before we speak. (This is weak, since the opposite point could be made, as the bells and pomegranates alternated).
See further here.