Mac disk full error but plenty of space

Solution 1:

Your fsck returned volume structure errors that disk utility can't repair.

You can use a utility like DiskWarrior to repair the directory structure.

Otherwise, an easier (but longer) method is to backup, erase the partition then restore the backup (the erase will setup a new file system with no damage). This works best via cloning the files (not the partition itself, that would preserve the issue) while booted from another operating system.

Another erase method would be to backup with time machine, boot to the Recovery disk (command-R during boot) and use disk utility to erase the partition. Use the installer to reinstall your OS then when it prompts you to restore a backup afterwards restore the time machine backup.