Hi Yves-Alexis, With another user bumping into this issue, I am keen to have it resolved in bookworm.
I think adding session optional pam_elogind.so to /etc/pam.d/lighdm-greeter is the best and correct fix. I know you have been reluctant in the past, but would you consider it again. Alternatively, I am happy to offer an NMU? Best wishes and thanks. Mark