I have connection issues with my Intel based network-controller on a pretty new DELL laptop.
The driver uses the e1000e kernel module.
I'm on stable Debian 11, with all patches and UEFI and firmwareupdates.

I also know it's not an ordinary network issue because I tried different USB Ethernet adapters, they all work. Also DHCP server is working fine with everything else.

To solve the issue I would like to enable the parameter "Debug" for the e1000e kernel module.

I have tried the following but I can't get the "Debug" parameter to work.
The system refuses to create the file /sys/module/e1000e/parameters/debug

Does not work:
sudo modprobe e1000e debug=16

Does not work:
/etc/default/grub
GRUB_CMDLINE_LINUX="e1000e.debug=16"
update-grub2

Does not work:
/etc/modprobe.d/e1000e.conf
options e1000e debug=16
update-initramfs -u -k all

Curiously this does work:
There is a file:
/sys/module/e1000e/parameters/copybreak
It has the default value of "256".
Using GRUB with the following parameter successfully changes the copybreak value in /sys/module/e1000e/parameters/copybreak
GRUB_CMDLINE_LINUX="e1000e.copybreak=128"

Any idea what else I could do to debug the NIC?

e1000e has a debug parameter, but the line:

creates it with permissions of 0, which means to not show in sysfs. I think you would need to rebuild the module to make it changeable (usually 0644).