Many thanks for your help albertoefg!
root user has a different config file that is not in /home but in /root
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If you encrypted disk and /home when you unlock at boot you are only
unblocking the disk but not /home
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Make sure /home is decrypted before startx
On the disk where the system is installed, I created /boot and left it
unencrypted, and used a whole partition where /home, /root and /swap were
created.
On boot, I unput my decrypting passphrase (twice), which is supposed to
unlock the partition containing /root, /home and /swap.
Then I input my account login and passphrase), where I land in a tty.
I didn't check the rights of the /home folder itself yet (though I did check
the its content, which is owned by me as the user, and it belongs to my
group).
