VGA ≠ HDMI / DP

I have this working well HP Prodesk 400 g6

- 10500t
- UHD 630
- BCM combo wifi/bt
- 16 / 512 go
- Ventura 13.6.6
- OC last release

Very happy with this stable hackintosh, I use it as Time Machine server and multimedia player.

I’m able to do anything I want with the VGA output: wake from sleep, disconnect and reconnect the cable, the signal will be back every time.

But for some reason, HDMI and DP are very problematic since I can’t boot if the monitor is not turn on before (it success to boot to the desktop but black screen if pluged/turned on after).
And of course black screen when waking up from sleep (it’s awake I can access via sharing screen).

Any idea where I can dig to be able to use HDMI the same way as VGA ?

Thanks for your help.