I have never seen anyone statically linking Qt anywhere, even with a commercial license. The main issue is iOS, where it's basically impossible to ship anything (L)GPLv3 on the app store, but that's due to Apple's lock-in policies.
Also, JNI requires you to use DLLs/shared objects, so you definitely can use them on Android.
> I have never seen anyone statically linking Qt anywhere, even with a commercial license.
from a quick grep on my hard drive, Telegram and QBittorrent statically link against Qt on Windows ; my own software also does, on all platforms. I assume there are others.
Also, JNI requires you to use DLLs/shared objects, so you definitely can use them on Android.