I just ran into this and am a little disappointed that this has been unanswered for 7 months and isn't already covered by the Alpine wiki.
- The command is actually
rc-update add syslog boot, not syslogd - If you haven't already, on Alpine < 3.17, you need to add openrc and busybox-initscripts with
apk add openrc busybox-initscripts. On Alpine >= 3.17, you can add a single packageapk add busybox-openrc