Using Debian 13 Trixie with kernel 6.12.69, the screen goes blank (no HDMI signal) as soon as it switches to framebuffer. 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.