Google Password Change Creates New Profile and Overwrites Mobile Game Progress

I have a problem accessing my old Google ID, which is linked to my Gmail account and used for a mobile game on my Android device. While I was playing, the game logged me out. Since two of my friends also had access to this account, I changed my Google password to secure it. After changing the password, when I try to log into the game with my old Google ID, the system instead logs me into a newly created ID with a new nickname, as if my old ID is no longer connected. Because of this, I cannot access my old ID and the game progress linked to it, even though I am using the same Gmail account. I have not yet been able to resolve this through any support channel. I kindly request that my access to the old Google ID associated with my Gmail account be restored so that I can continue using my previous game profile and data.