My ear doctor suggested the myNoise app[0] for me, specifically the Neuromodulator and Brown noise sounds.
The Neuromodulator[1] is a random-ish noise field that ... confuses? the brain after a while and lets you forget the tinnitus - at lest temporarily. The noise isn't "real" it's the brain generating it due to faulty signals, so giving it a bunch of noise helps somehow.
Brown noise[2] was specifically suggested for older people as it has more stuff in the frequencies we still hear naturally :D
As a happy coincidence my partner AND dogs sleep better with the brown noise on, they all tend to wake up to the smallest of noises - this helps with it.
[1] https://mynoise.net/NoiseMachines/neuromodulationTonesGenera...
[2] https://mynoise.net/NoiseMachines/whiteNoiseGenerator.php
I used to use brown noise, but I find that rain/ thunderstorm sounds are better. It's a noise that your brain is used to ignoring, and other sounds blend into it - even if they are almost as loud -while with the more homogeneous brown and white noise, it has to be louder than the sounds it's trying to mask.
Having said that, I'm not sure how well it would do for high pitched tinnitus.
Edited to add - now listened to the neuro modulator, nice one.