OK, I did some tinkering.
I downloaded the following Ubuntu kernel packages:
linux-headers-6.14.0-15_6.14.0-15.15_all.deb
linux-headers-6.14.0-15-generic_6.14.0-15.15_amd64.deb
linux-image-6.14.0-15-generic_6.14.0-15.15_amd64.deb
linux-modules-6.14.0-15-generic_6.14.0-15.15_amd64.deb
linux-modules-extra-6.14.0-15-generic_6.14.0-15.15_amd64.deb
And installed them on Debian 13/Trixie:
~$ sudo apt install ./*.deb
It installed fine and also built the initrd.
~$ sudo uname -a
Linux chromebook-flex-5 6.14.0-15-generic #15-Ubuntu SMP PREEMPT_DYNAMIC Sun Apr 6 15:05:05 UTC 2025 x86_64 GNU/Linux
~$ sudo lsmod | grep typec
cros_ec_typec 40960 0
cros_usbpd_notify 20480 2 cros_ec_typec,cros_usbpd_charger
typec 118784 2 cros_ec_typec,intel_pmc_mux
~$ sudo lsmod | grep pmc
intel_pmc_core 126976 0
pmt_telemetry 16384 1 intel_pmc_core
intel_vsec 20480 2 intel_pmc_core,xe
intel_pmc_mux 16384 0
typec 118784 2 cros_ec_typec,intel_pmc_mux
So the modules are loaded now, but still show the probing failure at boot:
~$ sudo dmesg | grep typec
[ 12.900605] platform GOOG0014:00: deferred probe pending: cros-ec-typec: Failed to register port 0
So I guess the modules are still not loading properly on Debian, even with the modified /etc/initramfs-tools/modules file.
However, manually unloading and loading the modules (like in the now obsolete systemd typec fix) looked promising:
~$ sudo modprobe -r -a cros-ec-typec intel-pmc-mux
~$ sudo modprobe -a intel-pmc-mux cros-ec-typec
~$ sudo dmesg | grep typec
[..]
[ 189.943821] typec port1: bound usb2-port2 (ops connector_ops)
[ 189.943874] typec port1: bound CON1-role-switch (ops connector_ops)
Now the external display is being detected when plugged in, but it still does not show any output:
~$ sudo dmesg -w
[..]
[ 1995.325870] ACPI Error: No handler or method for GPE 73, disabling event (20240827/evgpe-839)
[ 1995.365839] port1.0: EC does not support AP driven mode entry
[ 1995.365854] typec_displayport port1-partner.0: failed to enter mode: -95
[ 1995.443714] Registered IR keymap rc-cec
[ 1995.443843] rc rc0: DP-3 as /devices/pci0000:00/0000:00:02.0/rc/rc0
[ 1995.443971] input: DP-3 as /devices/pci0000:00/0000:00:02.0/rc/rc0/input24
The internal screen flickers for a moment and the Gnome control panel does show the external display though.
Any ideas what else I could do here (short of trying Arch Linux, which you recommended in the documentation in the first place)? The kernel doesn’t get much newer than 6.14, the required modules are present and reloading them has seemingly solved the problem in the past. I did not install Ubuntu’s linux-firmware package however, could that be the problem?