The attached image seems to show that there isn't a Audio device for indicating the HDMI output. It would be indicated as "High Definition Audio Device (HDMI)". The ones listed are for your speakers, headphone jack, and Digital S/PDIF.
For an NVidia or AMD card usually those outputs are always displayed, even when not in use or unavailable. Intel graphics drivers are more dynamic- as I understand it they remove and add the audio devices based on when they are available- for example when you plug into a TV it should then add it after it negotiates the HDMI version with the device.
I notice you have an added output, "Voicemeeter" and after some googling it appears to be from a product called "Voicemeeter Banana". Perhaps it is interfering with the standard audio featureset and preventing the HDMI outputs from appearing? Given what the product is intended for- and it directly manipulates those very audio devices, it may be preventing the Intel graphics driver from adding the device.