Aha! Thanks, Ken! So here’s what I’ve learned…
I noticed the following under the SEO / metatags section of the app settings on the free tier:
(BTW, that should probably say “Personal plan or greater” or simply “paid plan”.) However, it apparently applies not only to app-level custom headers but also to page-level custom headers, because that same JS snippet works fine in both locations on a paid plan. What’s perplexing is that there’s no indication at the page level that it won’t work on a free plan. Why not just disable or hide the field altogether to avoid confusion?
Anyway, something does seem awry with custom headers inside a plugin element - specifically, they don’t work - not even if the plugin is used in an app on a paid plan. That seems like a bug. How can a plugin be properly developed and tested if parts of it don’t work? I suspect this post is referencing the same issue.
Unless someone has some insights on this issue, I’ll go ahead and report it as a bug.