Disk full. Free space first, then find what filled it.
MySQL stopped, mail deferred, the site 500, SSH still up or already gone. We clear enough space to bring the service back, then remove the cause instead of deleting logs at random.
Not the website. The leftovers.
A PHP error loop, a mail deferral log, systemd journal with no cap. Safe to trim once the service is back, after a copy of the relevant lines.
Spam sitting in Exim, or local backup dumps that were never rotated. The queue is evidence. We do not flush it before seeing why it grew.
A binary log, an unpurged cache, a session table. Deleting the data directory is not a fix. A dump and a purge is.
Rescue, not a reinstall
A disk at 100% can stop sshd. On Hetzner, OVHcloud and the others we use the provider rescue system, mount the volume, free a few hundred megabytes, and boot normally. Reinstall is the last option, and only if you have a copy of the sites.
Emergency rate if the site or mail is down
A full disk with production offline is emergency, €95/hour, subject to availability. If the box is up and you can wait for business hours, it is standard at €55/hour, minimum 1 hour. Growing the provider volume is your click in their panel. We say if that is actually required.
Disk at 100%?
Tell us the provider and whether SSH still answers. Do not send the root password in the first message.