I don't understand what you mean by low-pass filter in this context exactly.

And what is the "cut frequency", as opposed to "sampling rate"?

It was just an example to show you a situation in which, past a certain sampling frequencies, there's no difference at all. It's very basic control theory stuff.

Underdamped oscillations happen even in simple linear systems when the controller is badly tuned, even if the sampling frequency is 10, 100 or 1000 times the one actually needed.

In GPB case, I wouldn't be surprised if the ECU is in fact designed as a bunch analog filters (plus some logic) integrated over time just like the bike dynamics at a very high sample rate (like 500Hz or 1000Hz, can't remember if PiBoSo ever disclosed this). If that's true, then there's no way to increase the sampling rate (unless one wants to increase the integration frequency even more).

Your reasoning (higher sampling freq = better AW) would be eventually valid if the AW was something as rough as "if pitch angle > 10deg then cut throttle to zero" and the sampling freq was very low (let's say below 10Hz). But hopefully in GPB there's something a bit better than this (but very likely not as good as a good modern AW). AW control is not that trivial on a real bike.

P.S.

If I recall correctly modders have very little AW parameters to play with (and I'm not even sure we have a clear description of what they does).

It's way more likely that the bad tuning (or plain bad AW algorithm) is responsible of poor AW performance.