@Rufledore
"..the bridge works fine only with the template project.."
Here I understand that you want to use this feature to create your custom templates. The feature currently is used only internally and this might be made available where power users can use this to create custom template components.
"..the lack of documentation related to that topic.."
Indeed, because the feature will be released with QDS 4.4 with documentation and example projects and complete Qt Quick Controls.
"...when we copy and paste, for example, MyButton template.."
This is indeed the correct way of using the Control Templates i.e. Copy and paste the complete set of control and then customize it as per your need. Unfortunately, the correct template code might be missing and the released version of QDS does not have the complete functionality to import the templates.