File this under “Learning the Hard Way” and “Stop Messing With Your Browser Settings.”
I was looking for something in IE’s settings when I stumbled upon cookie settings. (I still and only use IE with K2… it’s a habit from K2 4.x.)
My browser was set to accept third-party cookies, which is something I have disabled in my “actual” browser… so I did the same in IE.
The next thing I knew, attempts to view SharePoint pages with K2 SmartForms surfaced upon them were giving me a nasty error (“K2TSTS10002: An error occurred while processing a WS-Federation sign-in response”). This client uses K2 Cloud, BTW.
Reverting the third-party cookie settings fixed the issue.
TL;DR: Your K2-compatible browser must accept third-party cookies for K2 SmartForms to display in SharePoint pages.