Device authorization polling issue / question

Hi, im having an question to authenticating a device,
i have this function to poll for a token on the client:

```typescript
const pollForToken = async (deviceCode: string, initialInterval: number) => {
let pollingInterval = initialInterval;

const poll = async () => {
try {
const { data, error } = await authClient.device.token({
grant_type: 'urn:ietf:params:oauth:grant-type:device_code',
device_code: deviceCode,
client_id: 'my-app',
});

const { data: sessionData } = await authClient.getSession({
fetchOptions: {
headers: {
Authorization: `Bearer ${data?.access_token}`,
},
},
});

if (error) {
switch (error.error) {
case 'authorization_pending':
// Continue polling
break;
case 'slow_down':
pollingInterval += 5;
break;
case 'access_denied':
setIsPolling(false);
setUserCode(null);
toast.error(t('auth.deviceAuthorizationDenied'));
return;
case 'expired_token':
setIsPolling(false);
setUserCode(null);
toast.error(t('auth.deviceAuthorizationExpired'));
return;
default:
setIsPolling(false);
setUserCode(null);
toast.error(
error.error_description || t('auth.deviceAuthorizationFailed'),
);
return;
}
}

if (!data?.access_token) {
// Schedule next poll
pollingTimeoutRef.current = setTimeout(poll, pollingInterval * 1000);
}
} catch (err) {
setIsPolling(false);
setUserCode(null);
const errorMessage =
err instanceof Error
? err.message
: t('auth.deviceAuthorizationNetworkError');
toast.error(errorMessage);
}
};

// Start polling
pollingTimeoutRef.current = setTimeout(poll, pollingInterval * 1000);
};
```

it works ok until i call authClient.getSession, which sets only "better-auth_session_data" variable in local storage, but as i understand to get authenticated i need "better-auth_cookie" variable to have "better-auth.session_token" set, but i dont understand how it can be generated, which function / endpoint do i need to call after getting the access token?

thanks in advance

Start by tracing the device token call and authClient.getSession in the TypeScript client flow, then inspect how device authorization responses are converted into sessions and cookies. Confirm the expected storage and cookie state after successful polling, and document or test the endpoint or client entry point needed for an authenticated session.

Written by the indexing model from the issue text.