When I tried to register a new property using the Omeka S REST API, the following error occurred.

{ errors: { 'o:vocabulary': [ 'A vocabulary must be set.' ] } }

I then found the following thread, which mentions that adding properties through the REST API is not supported.

https://forum.omeka.org/t/programmatically-adding-properties-with-rest-api/7190

I hope this helps anyone else running into the same issue.