eBay have a history of lagging behind updating such price increases.

I think sellers on eBay would therefore respond with “Ha ha ha… NO.”

I shared your fears so I went on line with ebay and asked the question "Will my existing listings be updated autoatically and promptly?" This is the answer I received: "Yes, for your existing listings the changes would be made automatically and you do not have to do anything for this."  That seems clear but I will retain the transcript of the on-line chat just in case...