After some confusion, I think I’ve figured out that, if you change a document type in the Paperpile interface, then any further edits will not be synced to any Google Docs in which that document is used as a reference.
This might be the intended behavior, but I think it would be good to document this on the help/FAQ page. I had puzzled for a while about why my edits were not being synced to my Google Doc. In the end I reestablished the link by completely deleting the references from the Google Doc (including from the “all references” page) and then adding them again.
I discovered this while changing the document type I had used to categorise some grey literature, but I guess it could also apply to changing from “preprint manuscript” to “journal article” once an article has been published.