Hi. Thanks for your detailed question.
That shortcode actually “runs” the Event List Widget, which loads this file: /wp-content/plugins/events-calendar-pro/src/views/pro/widgets/list-widget.php
You could follow our Themer’s Guide to customize that file’s output, layout, etc. as you’re wanting.
We do not provide template override code for customers, per our Scope of Support / Terms, but using tribe_event_featured_image() in your template override is probably what you’re looking to do. As a starting point, you can reference https://github.com/moderntribe/the-events-calendar/blob/4.6.2/src/views/single-event.php#L58 to see how it’s used in the Single Event view.
Please let me know if you have any follow-up questions on this topic.