Is there an app for the Stack Exchange network for Windows Phone? I haven't seen any in the store, but browsing the site in edge it says, "read this post in our app". If there is no app for WP, couldn't SE recognize the client and suppress this message?
Not to my knowledge.
The reason it keeps suggesting an app is due to the way Edge is coded. It's coded to request the android version of web pages. The page detects a request from an android device, and includes the code to advertise their app and open the Play store link.