I'm kind of with Narcogen on this one.
The ONLY microphone you described in your setup is the external mic. Regardless of whether the audio is sent via HDMI, or not, that's the only mic you have.
In the FWIW department, I came to the forums today because I'm having an issue with audio being sent from my Canon Vixia HF g30, via an Elgato Cam Link 4k to my MacBook Pro.
Camera has a mini-hdmi out, which connects to the Cam Link, which then connects to the MBP. I record with an sdCard in the camera, as well as in OBS. The sdCard has audio, while the captured video does not appear to. :-(
I opened my Sound settings on the MBP and snapped my fingers in front of the camera while still tethered by HDMI and recording in OBS. There was a noticeable, albeit faint, movement of the bars. I then played some music on my iPhone, and cranked it's volume up maximum while placing the phone in front of the camera. This time the volume was captured along with the video just fine.
I then hooked up an audio cable directly from my Mac Mini to the mic input on the camera (which simulates what I do at my church) and played a song in iTunes. Came through just fine.
In my copy of OBS the MBP mic AND the Cam Link audio are being controlled by only one slider for some reason. (It's listed as "Mic/Aux").
Sorry, I can't point you to the Windows equivalent as I haven't used W10 in quite some time. But, I hope something of what I typed will help you. Seems like we both needed to just crank the slider volume somewhere. :-)
Robert
I know in some cases the HDMI connection contains both audio and video. The audio in this case would eliminates the echo effect of having the internal mic volume up