Does it happen during an update of the game? Or are you installing it for the first time?
During which step does it stay stuck? Checking update? Preparing to download the game data? or downloading the game data?
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Not much we can do there. If you don't have an error throwing, then you have to wait.
The whole process is painfully long, that's due to the way renpy handles the downloading process and the way android handles (or doesn't in this case) multithreaded reads/writes on its storage.
Your location can also affect the process, we only have two servers (EU and EAST-US), we're planning to deploy more but time is not the easiest resource to find.
I just checked a new installation on my Galaxy A13 (android 14) and everything works fine, it takes time but it works.