I took five sessions of HBOT ~2 weeks after my acoustic trauma. The tank/machine seemed quite old, yours look more modern and high-tech. I reckon there is quite a difference between models.
Anyway, as it was quite early after the trauma, I had hyperacusis and some parts of it seemed loud. The main part of sitting there after pressurization and just breathing in through the mask was very quiet, in my opinion. In fact, for some reason my T went away (or prolly quiet) every time as well, so it was closer to silence than outside of the tank... now that was wonderful. I have no idea why that happened temporarily while "under the pressure".
However, when the machine was actively pressurizing/depressurizing it was somewhat noisy. This took about 10-15 minutes, both at the beginning and the end, if I remember correctly, not 100 % sure.. Opening/closing the heavy tank doors made uncomfortable noise as well. Nothing damaging, I would estimate, though.
I didn't use hearing protection for the first and/or second time, but they had earmuffs which I then started to use, as I became worried about the noise. The audiologist said the machine kept at middle 70s (decibels) during active pressurization, but at least at the time it seemed a bit louder. But as said, most of the time spent in the tank was quiet. The 'breathing through the mask' sound was not irritating at all for me. I didn't get any adverse effects on my hearing or tinnitus.