Being expertise in daily work of MySQL and Linux. Ensuring to solution to your issue
The issue could be due to following reasons,
1. 5% (by default) of the filesystem is reserved for cases where the filesystem fills up to prevent serious problems. Your filesystem is full. Nothing catastrophic is happening because of the 5% buffer -- root is permitted to use that safety buffer and, in your setup, non-root users have no reason to write into that filesystem.
If you have daemons that run as a non-root user but that need to manage files in that filesystem, things will break.
2. It's possible that a process has opened a large file which has since been deleted. You'll have to kill that process to free up the space. You may be able to identify the process by using lsof. On Linux deleted yet open files are known to lsof and marked as (deleted) in lsof's output.
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