Using Debian 13 Trixie with kernel 6.12.69, the screen goes blank (no HDMI signal) as soon as it switches to frame buffer. With dmesg you can read the following errors:

[    6.587061] i915 0000:00:02.0: [drm] timed out waiting for [ENCODER:98:HDMI B] port ready: got 0xf, expected 0x0
[   16.775053] i915 0000:00:02.0: [drm] *ERROR* [CRTC:53:pipe A] flip_done timed out
[   27.015096] i915 0000:00:02.0: [drm] *ERROR* flip_done timed out
[   27.015122] i915 0000:00:02.0: [drm] *ERROR* [CRTC:53:pipe A] commit wait timed out
[   37.255074] i915 0000:00:02.0: [drm] *ERROR* flip_done timed out
[   37.255097] i915 0000:00:02.0: [drm] *ERROR* [CONNECTOR:99:HDMI-A-1] commit wait timed out
[   47.495072] i915 0000:00:02.0: [drm] *ERROR* flip_done timed out
[   47.495095] i915 0000:00:02.0: [drm] *ERROR* [PLANE:32:primary A] commit wait timed out
[   57.735072] i915 0000:00:02.0: [drm] *ERROR* [CRTC:53:pipe A] flip_done timed out
[   57.932964] i915 0000:00:02.0: [drm] fb0: i915drmfb frame buffer device

The only way to boot Debian 13 with kernel 6.12 is to pass the nomodeset kernel parameter.

It is possible to install kernel 6.1.0 from Debian 12 Bookworm, so that frame buffer works:

[    5.399065] fbcon: i915drmfb (fb0) is primary device
[    5.438998] Console: switching to colour frame buffer device 128x37
[    5.458533] i915 0000:00:02.0: [drm] fb0: i915drmfb frame buffer device

Despite the HDMI monitor is connected, the status pseudfile reports that it is disconnected:

cat /sys/class/drm/card0-HDMI-A-1/status
disconnected

Writing the on string to the file changes the status to connected:

echo on > /sys/class/drm/card0-HDMI-A-1/status
cat /sys/class/drm/card0-HDMI-A-1/status
connected

but it causes a kernel trace:

[   69.315446] i915 0000:00:02.0: timed out waiting for [ENCODER:94:HDMI B] port ready: got 0xf, expected 0x0

When the i915 kernel module is loaded, you can find five DRM (Direct Rendering Manager) devices managed by card0:

ls -1 /sys/class/drm/
card0
card0-DP-1
card0-DP-2
card0-HDMI-A-1
card0-HDMI-A-2
card0-HDMI-A-3
renderD128
version

It is possibile to do a complete hardware reset of the cards using the following command:

echo "0000:00:02.0" > /sys/bus/pci/drivers/i915/unbind
sleep 1
echo "0000:00:02.0" > /sys/bus/pci/drivers/i915/bind

After the unbind you can verify that the directory /sys/class/drm/ is empty, it will be populated again after the bind.

When the host is started in frame buffer text console, the setterm command can be used to force the screen to go blank (the monitor torns off due no signal):

setterm --blank force
setterm --powerdown 0

To revive the screen:

setterm --blank poke
setterm --powerdown 0