feat: update widget when settings are updated (COR-4159) (#456)

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**Fixes or implements VF-XXX**

### Brief description. What is this change?

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### Setup information

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### Related PRs

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- https://github.com/voiceflow/XXXXXXXXX/pull/123

### Checklist

- [ ] Breaking changes have been communicated, including:
    - New required environment variables
    - Renaming of interfaces (API routes, request/response interface, etc)
- [ ] New environment variables have [been deployed](https://www.notion.so/voiceflow/Add-Environment-Variables-be1b0136479f45f1adece7995a7adbfb)
- [ ] Appropriate tests have been written
    - Bug fixes are accompanied by an updated or new test
    - New features are accompanied by a new test

packages/chat/src/contexts/RuntimeContext/index.tsx

@@ -15,7 +15,7 @@ export const RuntimeProvider = ({ children, extend, ...settings }: RuntimeProvid
   const store = useRuntimeState(settings);
 
   // api is a static object, so we can use useMemo to prevent unnecessary re-renders
-  const api = useMemo(() => extend?.(store.api) ?? store.api, []);
+  const api = useMemo(() => extend?.(store.api) ?? store.api, [settings]);
 
   return (
     <RuntimeStateAPIContext.Provider value={api}>