Thanks! You are right, the /var/log/syslog file appeared after I installed the rsyslog package like this:
sudo apt install rsyslog
After that, the log messages are both in /var/log/syslog and the systemd journal, in the same way as on the Librem 13.
Unfortunately it does not seem to help with the sudden power-off problem, /var/log/syslog just contains the same messages as the systemd journal, still no clues to why it powered itself off. The issue I wanted to investigate is this one: When phone is warm it dies (abrupt power off) when charging cable is unplugged (#337) · Issues · Librem5 / linux · GitLab