And the likely reason why this is not happening (in the commercial space at least) is FDA regulatory hurdles in having a product (and probably an entire company) shut down for making "unapproved" medical claims.
I've got a set of Bose Hearphones, about $500, and which use the Bose Hear app. You can modify treble and bass but that's about it; even so if you are hard of hearing then the default iPhone sound profiles can be used to fine tune the in-ear audio and they work well as a low cost hearing aid. Same deal with my AirPods. Today Tim Cook could wave a magic wand and literally cure deafness for hard of hearing iPhone + AirPod users; ain't happening.
No question Bose Hearphones with the Bose Hear app or AirPods with a complementing iPhone app could easily perform spectral analysis with an easy-to-use-equalizer, to increase and/or decrease the amplitude of specific areas of the auditory spectrum; this would be ideal for tinnitus patients and would without question put the entire hearing aid industry out of business. Current generation hearing aids are about $15 worth of analog parts that they are selling for thousands of dollars each, just by virtue of having invested in some horseshit FDA regulatory process when infinitely more capable technology has been available to hearing impaired individuals for well over two decades at this point.
This is not complex, and what sucks about tinnitus is that it affects each person differently which in turn requires specific auditory tuning for each individual. But companies such as Bose or Apple that have the technology with more than sufficient computational horsepower to replace hearing aids simply refuse to do so, for whatever reasons that are likely FDA regulatory hurdle in nature.
On a side note as to OP, $300 for a Teensy-based hardware platform with BT stack is f'ing outrageous, probably worse than what the actual hearing aid vendors are ripping off.