Okay, so I started to look into this and I found the issue.
The child theme you use has template overrides of our calendar. I don’t know when these were put in place, but if some time ago, then most probably some of our templates were changed / updated meanwhile, and this hasn’t been reflected in the template override. It might be worth checking and comparing file-by-file if there are any changes, and adjust the template override files if needed.
The bottom line for the issue is in this file:
wp-content\themes\genesis-starfire-2\tribe-events\widgets\mini-calendar\grid.php
Once I removed that file, the heading of the calendar in the sidebar worked as expected: it showed the days of the week instead of the months of the year.
On solution is to remove (or just rename) this file in that folder, or if you want to keep the customizations you have there (I saw you have some but I didn’t check what they do), then do a thorough comparison and redo the template override based on the new wp-content\plugins\events-calendar-pro\src\views\pro\widgets\mini-calendar\grid.php file.
I hope this helps to get your site working as you need it.
Cheers,
Andras