The problem is in latest MIUI code which breaks Google's "Push Subscriptions" HIDDEN SYNC.
You can see this problem but you need ROOT + XPOSED.
Root your phone, install Xposed then Greenify (+ buy donation).
Open Greenify > Settings > Xposed-based Features > (scroll down in the "Require Donation Package" section) check/enable "Reveal Hidden Sync" > reboot.
Go to phone Settings > Sync > Google >
YourAccount@gmail.com > (scroll down, look for "Push Subscriptions", usually it'll got error (!)).
You can see the exact problem with latest beta + MIUI 9.5 update.
For some reason this hidden sync in Google's stuck & keeps syncing (this explain the high drain by Google services).
Don't follow this
http://en.miui.com/thread-2362847-1-1.html, it'll break your sync with Google.
ANOTHER FIX from GOOGLE: https://www.apkmirror.com/apk/go ... droid-apk-download/
Just install that, it'll fix the sync issue mentioned above. Don't ask me why.