Modify a theme to insert custom widgets?

As asked the question is quite broad, so I’ll provide a broad answer.

Unless the original theme provides its own hooks (which isn’t out of the question, and in which case you would need to consult its docs) the best way to do this would be to create a Child Theme, copy the relevant template to the child theme, and make the modifications there.

In terms of how to make an editable HTML widget in that template there are several options:

• Register a widget area using register_sidebar() in functions.php and output it in the template with dynamic_sidebar(). Then you can add the HTML with a Custom HTML widget.
• Use the Customize API to add a field to the Customiser for the HTML to go in and output it in the template with get_theme_mod().
• Add a custom field for the HTML and output it in the template with get_post_meta().

Ultimately though the exact approach comes down pretty much entirely on how the original theme was constructed. Some themes don’t work very well with child themes so you might run into issues trying to make changes that way, and other themes might offer their own hooks or APIs for making changes like this. It’s impossible to say without seeing its code. I would suggest contacting the developer of the original theme as a first step.