I once heard that when the talmidei haGro finally reached Eretz Yisroel, the talmidei haBesh”t were already there. As a way of making peace with them they accepted 4 or 5 things from the talmidei haBesh”t. One was V’sayn Tal UMatar. (I think one was sim sholom at mincha).
(I think birkas kohanim came from the Sphardim that were already there. It is known that the Gra wanted to reinstate birkas kohanim in Vilna but that he recieved a siman min haShamayim that he shouldn’t.)