Three useful states
A Live Activity can appear on the Lock Screen and, on Dynamic Island devices, in compact and expanded presentations. Good design treats those as different information densities rather than shrinking the same screen three times.
Glance first
The compact state should answer one question immediately. Expanded space can add context such as goal remaining or companion status. The Lock Screen can carry a little more without becoming a replacement for the full app.
Use the surface with restraint
StepIsland’s approach is to keep progress close while the person is moving, then let the full illustrated world remain inside the app where it has enough space to feel like a place.