The chicken coop controller needs access to use whatever drivers (Bluetooth?) to connect. On the other hand, they could have used Wi-Fi instead. The financial app, however, definitely should be a website. However, apps are a way to increase the longevity of the login token because apps on a non-rooted phone supposedly cannot leak the login token and can be trusted to keep it safe on the device.
oh wow, that's intricate but it probably works more reliably than something like a usb cable. Native apps probably have more control over framerate compared to webapps.
Bluetooth for example does work in web browsers though, and so does USB. There's web sockets and webrtc for communication. I can't think of a reasonable connection method that's inaccessible, but maybe I'm forgetting one.
I'd rather choose the password manager I trust that can safely store my credentials and auto-fill, than being forced to use a specific banking app with unknown security features.