Can I turn off the auto-closing of brackets in the editor?

Yes, you can choose whether the auto-complete feature will also auto-close brackets by using the settings menu in the editor.

Click the 'gear' icon in the top right to open the settings modal, and un-tick the box labelled 'Auto-Close Brackets' to disable this feature

Note: this won't affect any of the other auto-complete functions; these will continue to work normally.