I contacted support in BBedit and they came back with a reply which suggests to me that Affinity have some work to do to make Aff Pub fully compliant so that the copy and paste functions will work for us all.
Here is the relevant response,
Upon examination, I observe that Affinity Publisher is putting both 'public.utf8-plain-text' and 'public.utf16-plain-text' content types on the clipboard; however, it is populating the latter while leaving the former empty, and that is not appropriate: if an app _provides_ both types then it should also _populate_ them both (and since one can represent the same text in UTF-8 and UTF-16, there's no impediment to doing so).So, this discrepancy is responsible for why nothing happens when you attempt to copy text from Publisher and paste it into BBEdit, and I hope you find this info helpful.
How do we get Affinity to work on fixing this problem?