Hello @mathieu_pillar,
Thank you for looking into the kernel versions. I did a few searches as well and I saw a few different references to kernel version support but they tended to be older references that did not accommodate for the Ubuntu 24.04 support. There were a few fixes noted but I did not find very much that was conclusive.
I took a step back and I found one detail that I suspect I had overlooked before. For the next step I would suggest uninstalling the DisplayLink drivers, the dkms and libdrm-dev packages.
Once those are uninstalled, I recommend adding the Synaptics APT repository based on the instructions in the APT repository folder in the driver package.
The PDF document in the folder gives more detailed instructions including instructions to reinstall those after the repository is added.
Please let me know if that helps!
Sincerely,