Ah yeah the easiest way is probably using the OpenTelemetry collector to set up a process to pull your logs out of jounrnald and send them via otel logs to HyperDX (or anywhere else that speaks otel) - the docs might be a bit tricky to go around depending on your familiarity with OpenTelemetry but this is what you'd be looking for:
Actually I am not really using syslog per say, but systemd journalctl which default behaviour on Debian (rsyslog) also duplicates to /var/log/syslog.
Is there a better integration to pull logs from my systemd services and journalctl up to HyperDX?