When you say "switch to mobile view" - are you referring to turning off the 'Request Desktop Website' setting for Safari?
Mobile view was the default on Safari for iOS on iPads prior to version 13. For version 13, Apple, in their infinite wisdom, decided that iPads would essentially be desktop devices. Thus iPads now use "iPadOS" not iOS. Full desktop view is now the default for Safari on iPads and the option is to override that and request mobile site. Drag and drop seems to only work on the mobile version and since the default is now desktop, clients require manual intervention to see interactions like drag and drop.
OK - but in the settings for Safari on the iPad there is an option to turn off the desktop request.
I was wondering if that is what you meant -
Yes, that's it exactly.
Did you find a solution? i'm having the same problem.