Update: We received this official response from PayPal. Unfortunately, it does not confirm or deny it is working on a Windows 10 Mobile app:
We recently announced we will no longer be supporting the Windows Phone version of the PayPal app as of June 30. We have nothing more to share at this time about potential future app versions but Windows Phone users can still access PayPal through our mobile web experience on Internet Explorer and Microsoft Edge browsers.
As previously announced, PayPal shut down its Windows Phone app on June 30. However, people who opened up that app today got a message that indicates a new version is "on its way":
While this in-app message is no guarantee that PayPal is in fact working on a Windows 10 Mobile app, it's certainly very promising. We have contacted PayPal to see if they will comment on any future developments in this area.
Thanks to Mark for the tip!