In few themes it is observed that the template parts are having a theme attribute set. This causes the template part to no render in the site frontend and editor.

<!-- wp:template-part {"slug":"secondary-header","theme":"jaida"} /-->

Error in the editor:

Template part doesn't render in the frontend:

Tested by creating a blank theme and exported. It doesn't create any such attribute.
Need to understand the theme creation process from the designers to check if this is still an issue.