Duncan, sorry for the delay.
I didn't get a notice of a reply. Hopefully you have this working?
On AGOL, you go to the hosted layer and Settings. I'd imagine you figured that out.
I think the confusion on the publishing side is that I initially published my hosted layer to AGOL via ArcMap and not ArcPro. In ArcMap, when publishing the service, in the Feature Access dialog box, one of the Operations allowed is Delete. I think if you don't have this checked then you won't be able to set the same up on AGOL.
In ArcPro, you have to click on the Configuration tab of the Share as Web Layer and then Enable Editting and "
Add update and delete features"
Hope that helps.