Thanks for the feedback! Seems like an important point that the lowest volume is inaudible to most (?) users. To me, the "warm noise" sound is the only one that allows for sleeping on the lowest volume (I can actually manage that on the second to lowest volume too).
I've got used to using "warm noise" in my apartment, where there is a great deal of background noise, but when I'm on the countryside, the sound level gets tough on the lowest step there as well.
Before Bose created their product there was the startup Hush with the same concept. I bought a pair of those and had the same problem with the sound level, so there is a risk that my hearing is simply too "good". Perhaps I should try to switch to a new pair anyway.
I've been in contact with Bose support, and unfortunately, they have no idea about how the volume system works in their own app or how to lower it.
A quick update on my quest to lower the volume: I changed my sleepbuds in the store to a new pair, but they have the same problem. The volume is too high with even the softest sound for me to sleep comfortably.
I've found out that it's possible to lower the in-app volume slider manually, without using the volume control buttons on the phone, but all sounds except one are still completely useless, and the one I can use (warm noise) is too high for comfortable use most sleeping environments.
After waiting more than a month, I finally got a reply from a guy at Bose Support who are willing to look into this matter, so I'll see if he can come up with something.
I paid the equivalent of 350 USD for the product, and this volume problem seems to me like a very trivial thing that should not be possible for a product priced over 35 USD. There is to the best of my knowledge no cost involved for Bose in making the lowest steps of volume really low so that the product is useful for sound-sensitive people, and I think that the manufacturer of a 350 USD product should have taken this into account, or at least been able to recommend some trick for externally lowering the phone playback volume that works for their app.