Trouble with embeds after upgrade to 4.5

Ever since I upgraded my sites (both production and development) to 4.5, any WP embeds have stopped working. I have tried switching my themes to Twenty Sixteen and disabled all plugins but the problem remains. Instead of showing the embed, there is just a plain URL.

I’ve been trying to debug this myself and it looks like wp_oembed_get() is returning false.

Here is an example URL that has a custom embed templates that I’m trying to embed on other sites:
https://www.ednc.org/flash-cards/singapore-north-carolina/

Not sure what information I would need to provide for troubleshooting, so please let me know. I appreciate any and all help!