as I hinted in my previous post, I fixed a problem that I had which seemed to influence also the stability of Bluetooth HID by "Installing Default Apps" from the App Loader. I can't say what exactly the problem was, I somehow messed up the storage and maybe some important firmware parts with it, but afterwards it was much more stable.
That said, I still occasionally encounter these same issues (repeated keystrokes or no keystrokes registered at all), like maybe once out of 10 times. It's not the reliability of a wired solution connected via USB for example. I never used a Bluetooth device before, but my assumption is that's just how Bluetooth works and not necessarily a fault of the Bangle.