The closest I know of is GPT4ALL which @[email protected] recommended on one of my posts. However (1) it does not use your OpenAI key but rather runs everything locally on your device, and (2) it cannot search the web out of the box. It does have plugin extensibility however.
The next closest I can think of is Perplexity which is connected to the internet and can chat based on files/documents. This one is not open source and still doesn’t use your OpenAI key, but it is free to use.
Both of those options are 100% free with unlimited use.