Inode exhaustion in session directory

An internal admin portal starts failing logins at 11:00 with 'No space left on device' whenever it writes a new file-backed session, but df -h shows the data volume at 47% used, gigabytes free. The host has been up 90 days. df -i shows the volume at 100% inodes. The session directory holds tens of millions of ~200-byte files. A cleanup cron exists but find /var/sessions -mmin +120 -delete has been running for hours without finishing, and load is climbing. There was no deploy; sign-up traffic has been slowly growing for months. How do you triage and recover safely?