Hello Nicolas,
(Warning: I've never really tried to modify the LightDM setup and I
presently use gdm3)
Perhaps you will find answers on the GIT page of LightDM (section
"Configuration"):
https://github.com/canonical/lightdm?tab=readme-ov-file#configuration
and on this page which details all LightDM possible options:
https://github.com/canonical/lightdm/blob/main/data/lightdm.conf
user-session is not set in Debian LightDM setup: if you want the default
session to be the last, perhaps you can try assigning "last" value to it
(I don't know, I have tried it)