I compared /etc/pam.d/sshd of the affected and working system, they are identical. But, I
found these entries in /var/log/secure of the system in trouble:
error: ssh_selinux_setup_pty: security_compute_relabel: Invalid argument
I bet it's a smoking gun, I just have no idea what to do about it.
Sincerely yours,
Vadym Chepkov