Sure. I think what you're looking for are "AI agents" or "RAG" (Retrieval Augmented Generation). It's not the model itself that does it, but the framework and software around it that provides the internet search capabilities.

And it's not unique to ChatGPT. It's been available also to open-weight / local models for years. I've lost track of all of the frameworks we have and what features they have. So I don't know what to recommend. But you can look it up, there are several frameworks available that provide such capabilities to any model. Maybe your preferred solution even has a plugin available.

The underlying method is probably the same for how ChatGPT works internally, and all the other ones. And it's related to how companies have always fed internal data to their chatbots since all of this started.

You can try one example on hf.co/chat Another solution would be something like h2ogpt. It can do web-search and also index all of the PDFs on your harddrive and answer questions about them and do vision tasks, look at pictures or generate them.