pdns_recursor stats logs are seen in journalctl but not in /var/log/*.
As journald doesn't save to disk this means all logs are lost on reboot.
pdns log facility is 3 (daemon) and priority (=syslog severity) is 6, this translates to daemon.info
Mon 2019-06-24 12:26:51.084882 CEST [...] _BOOT_ID=xxx _MACHINE_ID=xxx _HOSTNAME=vyos _TRANSPORT=stdout PRIORITY=6 SYSLOG_FACILITY=3 SYSLOG_IDENTIFIER=pdns_recursor MESSAGE=stats: 54106 questions, 4436 cache entries, 997 negative entries, 6% cache hits _PID=2868 _UID=0 _GID=0 _COMM=pdns_recursor _EXE=/usr/sbin/pdns_recursor _CMDLINE=/usr/sbin/pdns_recursor --daemon=no --write-pid=no --disable-syslog --log-timestamp=no _CAP_EFFECTIVE=404c1 _SYSTEMD_CGROUP=/system.slice/pdns-recursor.service _SYSTEMD_UNIT=pdns-recursor.service _SYSTEMD_SLICE=system.slice
vyos default for /var/log/messages is *.notice;local7.debug
By setting set system syslog global facility all level info; set system syslog global facility protocols level debug, from short testing on my machine, it adds dhcpd and sudo logs which you'd want saved anyway, so imo the default should be set to *.info. This does increase disk writes so it may not be suitable for flash drives.