The notch filtering mechanism is the ‘old’ way of doing it, but still forms the basis of some systems (Resound etc). You’ll see that the aids just wind in the HF gain on a REM screen when there’s a pure-tone detected - even if the source of the pure-tone isn’t the aids themselves.
There was a previous post where somebody said that they had the gain turned-up and it made no difference to the amount of feedback: it won’t, as the aid will still cut the gain at the same frequency. The impression of loudness tends to come from below 750Hz while feedback tends to peak around the resonant frequency of the receiver unit (and ear canal) at around 2.5-3 kHz.
Other aids use sine-wave inversion, frequency shifting, sound tagging and binaural recognition to reduce the effect of feedback.