session.glasses reports on the glasses hardware: battery level plus charging state, and whether the glasses are connected. Both are subscriptions, so you get a callback whenever the value changes.
src/background/index.ts
There’s no synchronous getter for the current value. You learn the state by subscribing and waiting for the first event.

Battery

onBattery fires when the glasses report a new battery reading.
Each BatteryData has:

Connection

onConnection fires when the glasses connect or disconnect.
Each ConnectionData has: modelName is optional, so guard for it before reading:

Cleaning up

Both methods return an unsubscribe function:
session.glasses covers the glasses hardware. The phone has its own battery and connection events on session.phone. For what the connected glasses can do (display, camera, sensors), read session.capabilities once the session is ready.