DigitalOcean Ubuntu Droplet NGINX Security Patch / Check

We have a DigitalOcean Droplet running NGINX. DigitalOcean has advised our NGINX version may fall within an affected vulnerability range, but they cannot confirm whether Ubuntu/Debian backports have patched it. We need someone to: SSH into the Droplet; confirm OS version and NGINX package version; run safe package updates for NGINX/security packages; confirm NGINX restarts cleanly; check basic NGINX access/error logs for obvious suspicious activity; confirm whether automatic security updates are enabled; avoid making website/application changes unless agreed first; provide a short written summary of what was done. This is urgent but should be a small sysadmin/server maintenance task.