So after a lot of research, I found out the reason and the way to fix it.
I noticed that I was able to do 4K@30Hz HDR but not 4K@60Hz HDR.
So what I did was to use the Custom Resolution Utility to inspect things at adapter level.
After clicking edit on the Extension Block CTA-861, I noticed that for some reason, the Lindy dongle was reporting support for just HDMI 1.4:
So what I did was to click Add... in that menu and add a new HDMI 2.x block and click ok:
And that allowed me to do 4K@60Hz HDR.
I also think that although the Lindy adapter doesn't support it since it's HDMI 2.0, someone can go even higher at 120Hz with this method by just adding a HDMI 2.1 feature like Maximum FRL Rate @ 48Gbps. That will enable the graphics card to send using HDMI 2.1 so that the software like Moonlight can capture it even if the adapter doesn't support it. Of course, I suppose, someone would need a graphics card that supports HDMI 2.1 like the RTX 30xx series.
