What happens if the companion phone battery dies?
Features that depend on the phone lose that part of their workflow. The glasses may still have power, but a live companion link, phone-hosted app or internet relay cannot continue through a powered-off phone. Local behavior is product-specific.
A lit display does not prove a live service
Make the loss of connection visible and distinguish any remaining saved information from a current result. Otherwise the last card can look reassuring even though it is no longer updating. Battery state is therefore also an information-freshness issue.
If the display holds a departure time, a dead phone may prevent later updates from reaching it. The app should label the time as last received information rather than silently imply it is current. For an important task, keep an alternative way to obtain the information when the companion is unavailable.