I'm just getting K2 configured on my site and I have been previously using Joomla's "Articles Category" in "Dynamic Mode" so that I can create a single module that displays on every page and shows a list all of the other articles in the category that the current article is in. I need to be able to display an "In this section" list that changes per category that you're in.

I found this tutorial (from back in the day) which is interesting, but I need a single module that will do this. www.slurpitup.com/joomla/how-to-add-related-items-by-category-in-k2-joomla

Hi. There is no built in module in K2 which can do this. You need to either find a third-party module or use the multiple K2 content module instances.

Are there any recommended modules which do this?

No, i am not aware of such a module. You can take a look at the K2 extensions directory at getk2.org/extend.