What is the /oem partition? Recently I had an over-the-air (OTA) update fail because the /oem partition did not pass the assert. However, it looks like the update still "succeeded" in that the /system partition had all the updated bits and the update check in Android says I'm at the latest version. I'm guessing my /oem partition is outdated now but it doesn't seem to be affecting anything.

What is the purpose and capabilities of the /oem partition?
The /oem partition is used for any carrier customisations to the Android firmware; if your firmware build is not a carrier-specific one then it might be empty anyway.  This purpose is described in the Android Project Treble documentation.