The I18n translation is the core library to provide mulingual support.
You can read about that in the hugo docs about multilingual sites.
Your theme does translation on then theme components only. Thats not multilingual. And the docs say nothing about i18n support.
All that code is hidden in the themes source.
Theres also no doc about creating your own widgets. Maybe the theme author is willing to assist.
If you are already on the way to customize the theme…well just adding somthin to i18n won’t do it. You will have to study the themes code of an existing widget and adapt for your new widget.
Guess they have something like a simple lookup table and partials somewhere.