Clearly one of those, "I could be missing something really obvious," issues. While not shown here, my statement to add the facets block was adding it to the overall post object (this.facets = { ... }). But the facets block should be added to the record block (this.record.facets = { ... }). Now that I've made that update, the hashtag is appearing as expected.

Now to see if I can extend that to mentions and links.

Thanks to a reddit user for helping with this one.