The output gain on the Audio Outs settings of the device is a post DAC (Digital to Analog Converter) gain stage, in other words, is a gain control when the audio signal is already converted to analog.
The Headphone Volume is practically the same, but for the headphones amplifier.
Then on the Output Processing Settings, you have the Pedalboard Out Gain. We must say that we had recently a few talks about this and even internally this setting was leading to some confusion there may be some changes on this soon. Anyway, currently, this setting controls the signal volume still in the digital world. It works sort of like the gain plugin that is set on the default pedalboard just before the out-ups (the only plugin loaded when you create a new pedalboard). Yet, in this case, this gain stage comes after the output compressor in the chain, in case you have it activated.
A little side note, it was a pleasure to receive you in the office and get to know you personally @llorenzo
Is it possible that something happened in the support notifications and I’m not aware of your follow-up? In other words, am I owing you an answer and I didn’t really request you more time to give it to you?
Sorry to ask you here, but the “million things” as you mentioned sometimes make it hard for me to remember exactly a particular case.