While you told cron where to find bash using an absolute path, ".local/share/script/fan_script.sh" is still a local/relative path. Try "@reboot root /bin/bash .local/share/script/fan_script.sh > /dev/null 2>&1
@reboot root /bin/bash /root/.local/share/script/fan_script.sh
", with a heading "/" = a "full path" if ".local/" is inside of "/root/"...Good luck

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