Hello elektrafestival,
Thanks for going Pro and welcome to the forums!
I see where you are coming from. I might be able to help you with this.
By default the ‘Default Event Template’ does not have the sidebar regions incorporated. If your theme has them for the pages, then it should be easy. Just switch from ‘Default Event Template’ to ‘Default Page Template’.
If your theme’s default page template uses sidebars, then with the above setting your calendar pages will do too.
Try and let me know if that does the trick.
Cheers,
Andras