I tried to do exactly what you did and overwrite the mod with original to sign in Google which installed perfect but as soon as I opened up the game again when I installed the mod, the game makes a check and says you have no internet connection and wipes the Google login and you're forced to use guest mode only. I searched extensively for the save files data in android/data as well as data/data and used multiple apps that can back up all your apps and data and still couldn't find the save data saved locally.
Interestingly if you do play on guest mode and then uninstall the game completely and do a fresh install, the game can still find the guest mode data and load you up at the same point you was at previously which brings me to the assumption that this game can check your device ID so whenever you do fresh installs it has your device ID save data in their servers. This of course also means if you cheat and get banned it's gonna be really hard to play this game again on the same device. Playing the game in a different virtual emulator might solve this issue because then the game will think you're on a different device entirely but I exercise caution logging in Google on original apk and overwrite it with modded to take advantage of your Google account because from my experience it doesn't work and the game will just wipe the save and there is no way of getting it back again unless you're prepared to play unmodded the whole time which is a tiresome experience when there is such high difficulty levels and arena starts churning out opponents that have way more power than you.