Yes, an hearing aid is a microphone + adc + dsp with EQ , compression, limiter, + dac + amplifier + speaker

All this battery powered and very small, and need to process almost realtime

it is like have a full homestudio in your ears

I don't know if they have improved and created hearing aids for musicians today, as the main goal is to help people to listening speech voice mainly amplifying in the 1000-6000 hz range