Following latest React Native setup steps, crashes with "_clientCommon.createNullLogger is not a function (it is undefined)" from browser.js

## Description

[Following the latest setup steps](https://www.algolia.com/doc/guides/building-search-ui/installation/react/?client=React+Native) for React Native, I get an error when initializing the `liteClient`.

## Reproduction
Follow the React Native steps

Code:
```typescript
import { liteClient as algoliasearch } from "algoliasearch/lite";

const searchClient = algoliasearch(ALGOLIA_CONFIG.appId, ALGOLIA_CONFIG.token);
```

package.json
```json
{
"react": "18.2.0",
"react-instantsearch-core": "^7.15.3",
"react-native": "0.74.5",
"algoliasearch": "^5.20.2",
"expo": "~51.0.38"
}
```

If I reduce the algoliasearch version to `4.24.0` and change to not import from the lite client, it works.

Reproduce the crash using the linked React Native setup and the versions listed in package.json, starting with the liteClient initialization. Trace the failure from browser.js and verify that the documented import and initialization complete without the createNullLogger error.

Written by the indexing model from the issue text.