Feature Request: Add Copy Page Button for people + LLMs

### Have you read the Contributing Guidelines on issues?

- [x] I have read the [Contributing Guidelines on issues](https://github.com/facebook/docusaurus/blob/main/CONTRIBUTING.md#issues).

### Description

This is all the rage now. Example: https://mintlify.com/docs/quickstart

Ideally we could have the same options, or a configurable set of LLMs.

Considerations:

1. Need to strip comments and images from final markdown before it's exposed to people.
2. Could either load the whole thing into the built page as data on the copy button, or use the mintlify approach of building a clean .md exposed publicly.

### Has this been requested on Canny?

_No response_

### Motivation

Getting popular in doc systems.

### API design

_No response_

### Have you tried building it?

_No response_

### Self-service

- [ ] I'd be willing to contribute this feature to Docusaurus myself.