I was unaware that the new text style pertains to only the document in which it was created. It would make more sense (to me anyway) for that text style to remain in the text style menu so it could be used on other documents as well. I'm applying English text, in the same style, to a non-English comic that has been scanned, so every page is a new document.
Importing text styles only makes the desired text style available to the document in which it has been imported. I want it available to all documents.
The only other alternative was to make the text style the default text style, which is what I did. Unfortunately, that wasn't a total success. I can get the text style to appear in the styles menu in new documents, that is, documents created in Affinity Designer, but not existing ones.