Since updating to iOS 17 there doesn't seem to be a way to automatically open files AirDropped into any applications. The files get downloaded to the Files application and you can open them from there, but previously you could open them straight in another application. There doesn't seem to be any documentation to this change.
Is there still a way to open AirDropped files directly in a non-Apple published application?
On iOS 17, the behavior of saving an AirDropped file to the Downloads folder (and then launching Files.app) is intended. That is part of the effort to avoid directly passing a file to an app that declares itself as a handler of the file type but isn’t really the file handler that the user expects. If you have feedback on the behavior change on iOS 17, feel free to file your feedback report <http://developer.apple.com/bug-reporting/>.