I downloaded the latest experimental build APK just now, and unfortunately, the issue is unchanged. Failed to mention that my mobile device is a Sony Xperia, so the way it configures the controller may be different?
As I test at the moment, indeed the app for me also only registered the directional buttons and the left joypad for my PS4 gamepad when keybinding. It does definitely know all the buttons exist, though, as pressing each button while in game returns "Unknown command: “UNKNOWN [number]” in the log. I suppose I could fiddle around in the keybindings.json to manually add keybinds, but it wouldn’t have the functions I use on PC (modifier button, tap/hold).
Thanks for your reply and help. I didn’t find any workable apps on Android to map buttons to keys, but hopefully you have more luck.