Thanks for reaching out, Matt!
So, sidebars are not dictated by calendar views at all. This is dictated by your theme templates. What you can try doing is going to Events → Settings → Display in your site’s wp-admin and looking for the Events template option there — these are all various templates that your theme provides. You can try all of the different options here and see if any specific template provides a sidebar.
If you find a template that provides a sidebar, then:
• Yes, you can add any calendar widgets you’d like. You can learn more about available widgets by checking out related Knowledgebase articles here → https://theeventscalendar.com/knowledgebase-tag/widgets/
• However, you cannot use the [tribe_events] shortcode in a sidebar on the same page as a main calendar view. The [tribe_events] shortcode generates a full calendar view of its own, and only one full calendar view is allowed per-page, so you cannot have a main calendar view like the List View with filters and such, and then also add a [tribe_events] instance on the page anywhere.
I hope this helps!
George