I noticed not everyone know this yet, so I'll drop this little guide here.
I've reinstalled Project Sekai for a dozen times also often to play it on my other phone, without need to worry about losing my progess.
Login method of this sekai is Google Acc, and have been always back up your progess automatically.
So I always do this after reinstalled sekai :
That's how I login my progress.
Important note : If you aren't newbie, and just reinstall the game like I did above. Keep in mind to always log in first so you don't download excess data from the tutorial session.