What I found that helped was to create a custom Shortcut that "Set Media volume to 1%". iOS reports that this is 48 dB when playing pink noise. I managed to hit 47 dB when dragging to volume slider on iOS below 1%, but the Shortcuts app only seems to support integer percentages.
In my case, even the 1% volume level was too high in a quiet room, but some apps have a custom EQ setting that you can use to lower the volume further. E.g. if you're using Apple Music, you can go to Settings -> Music -> EQ and pick "Loudness" to lower the volume further.