Interesting, seems like you’ve done a lot of testing. Have you updated your Slang Shaders using the Online Updater? The Sony Megatron Color Video Monitor had some nasty bugs a couple versions ago which would actually prevent HDR from being enabled when using the Vulkan Driver. It would have still showed up in the menu though.
After updating you can possibly try other cores besides the Mame core and see if the behaviour is the same.
You can also try backing up your RetroArch.cfg file and starting over your configuration from scratch or backing up your entire RetroArch folder then try a clean RetroArch installation.
You can also try reinstalling your Intel IGP drivers.
You can also try the D3D11 and D3D12 drivers as well or even GL_Core to see if they will make a difference because they are all supposed to support HDR in RetroArch as well. So that might work if there is an issue with Vulkan on your system especially since you said that HDR works in Windows.
If using any of the D3D Drivers or if you’re on Windows 10, you will have to also enable HDR in Windows before launching RetroArch for the HDR option to even show up.
I think this is something that should be brought to the attention of @MajorPainTheCactus in case there’s some bug involved.
Maybe someone else with an Intel IGP can test as well.