The log shows this:
08:49:48.595: coreaudio: failed to find device uid: com_blackmagic_design_iokit_DeckLink_AudioInputEngine:0, waiting for connection
It looks like you've been trying to add your capture device as a Blackmagic device in some instances, and as a Video capture device in others. As the latter, I think you may need to also add it as an audio source.
I honestly don't remember whether the Ultra studio mini is supposed to be added as a Blackmagic device (which is for Decklink cards mostly) or just as a generic video capture device.
Also check the advanced mixer to make sure your audio devices are assigned to the track you're streaming (or all tracks if you're using simple mode and not recording discrete multi track audio).