You are in your app, ready to start training, but you cannot pair your Neo. It does not appear in the pairing list at all. You have confirmed that Bluetooth on your device is enabled, and it is definitely working in other apps.
In iOS 13, apps that can control your trainer have independent access options to select features of iOS, including Bluetooth. If the Bluetooth option is disabled for a particular app, Neo will not appear in the app’s pairing list even though it’s working normally elsewhere.
To enable Bluetooth for any particular app, open the Settings app on your iOS device, and scroll through the apps list on the left side of the screen. Tap on the app title, and the options will appear in the right pane.
The fastest way to see the list of apps with Bluetooth access, and to enable or disable that access, is through the Privacy menu in Settings, and selecting the Bluetooth option.