Short Answer: Search Settings for "documentation popup" and either un-check the option to disable the popup, or increase the delay
After some recent upgrade to Android Studio -- I think it was to 3.6 -- I started seeing the Documentation window/panel automatically popping up as I was coding. There was no obvious way to stop it, but I found an option in Settings:
Settings -> Editor -> General -> Code Completion -> Show the documentation popup in ____ ms
I wish this setting could be controlled directly from the little gear icon that's on the Documentation popup. I tried "Remove from Sidebar", but that doesn't prevent the popup from reappearing.