Hey @christopher! You seem to be missing the extra code on the page.
For this combo to work you need to add defer fs-attributes-preventload="true" to the CMS Tabs script on the <head> and this callback function for CMS Nest in your </body>.
Can I ask where in the documention I find this info (for the next time)
Also: I have added some embed blocks in the nested collection item. These are not loading in the nest parent, but they work fine if I use them outside of the nest.