I tried to remove the Bitcoin app from the device in order to reinstall it. But Ledger App manager won't let me do it (operation fails).
Did you try to remove an application before trying to reinstall the BTC app again?
It sounds strange, but sometimes there just isn't enough space on the nano s (even if you had the app installed already).
Just uninstall an application and try to install BTC app again. The amount of applications which can be installed at the same time on the nano s varys from 3 to 5.
This depends on the size of the application. The fido u2f app, for example, is one of the biggest.