The bottom button, closest to the tip, does nothing when pressed

Probably an eraser button, as in switches the tool into eraser mode?

The top button, when pressed acts as a back button.

Run libinput record --all and see what kernel event that button produces and off which event node. My guess is that this isn't just a stylus button but has its own behaviour like e.g. most BLE pens.

Data matches up with the auto-generated version, so looks good to me 👍

The button configuration issues need to be fixed by GNOME. I have a pair of issues open for them at https://gitlab.gnome.org/GNOME/gnome-control-center/-/issues/1020 and https://gitlab.gnome.org/GNOME/gnome-control-center/-/issues/1021

Probably an eraser button, as in switches the tool into eraser mode?

Yup, the button closest to the tip looks to be an eraser mode with event BTN_TOOL_RUBBER.
The top button seems to be just a stylus button, BTN_STYLUS. There is another event listed BTN_STYLUS2 but I wasn't able to find out what it does or how to trigger the event.

merged, thanks