RTX 3060: no HDMI output (blank output)

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Hi,
I have a strange issue with HDMI and a ZOTAC RTX 3060 (12G)
The card comes installed in a ZOTAC MAGNUS ONE (https://www.zotac.com/us/product/mini_pcs/magnus-one-ecm53060c-barebone#spec)

The issue is simple: no HDMI video output (tho, video signal seems to be detected)
Here are some notes:

- no issue with DP
- no difference with Windows 10 and 11
- no difference with 1 year old video drivers and latest ones
- no difference with various HDMI cables
- if I boot with DP, then in Windows I unplug DP and plug HDMI still does not work
- if I boot with HDMI, I can see the Windows loading logo for few seconds, then when it switches to login I see only black screen (but the signal is still detected on display)*
- I have the same behaviour with 2 different monitors and also an LG C1 OLED TV

Any idea? Maybe this is something common and I forgot to enable something in NVIDIA drivers?

* this seems to point to some kind of driver/firmware/setting related issue (?)

OK I dug deeper and found the problem

The short version is that HDMI video output works just fine without NVIDIA drivers and keeps working only if you install the drivers while you are connected over HDMI.
It doesn't work if you install the drivers using DP and then connect over HDMI

This happens only with this specific ZOTAC card, it doesn't happen with the Gigabyte RTX 3070 I have in my main, which I installed and always used over DP, but when connected with HDMI works just fine