There is already a request to have read-only mode shown to users of the iOS app when the site is read-only. I'd like to also request that the app actually direct users to the canonical / official status resources that are maintained when network errors arise:
Ideally, these links would also be in the help section as links or if the app can actually consume the data posted, but the app currently (v22.214.171.124) draws a blank blue screen when starting up if the API is down and/or DNS is not resolving due to network errors. It also has a black failed message if the app was working and cached some data locally before the site outage starts.
Neither of these current iOS app indications allow users of the app to find the cause of errors or start troubleshooting if the app is broken, their network is broken or the end point services are broken.