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Have you check the Package.GetAppInstallerInfo Method and the Package.CheckUpdateAvailabilityAsync Method?
The first one could get the URI from the .AppInstaller. If a user who already has the app clicks the URI, the app is updated if needed and then it opens. If a user who doesn't have the app clicks the URI, they are taken through the install process for the app.
The second one could help you to check if an update is available from the server indicated in the .AppInstaller.