[DOC] Add copy-to-clipboard LLM prompts for creating custom estimators and for other purposes

Describe the issue linked to the documentation

Sktime implemented extension templates even before LLMs existed. These templates have turned out to be very useful for LLM-based workflows, especially when additional information is provided—such as example source code from similar estimators.

Nowadays, it is increasingly common to use LLM tools to support the development process. Having some copy-and-paste prompts for different goals could be very helpful for new users and practitioners.

I’m creating this issue to propose and discuss the addition of a section in the documentation—or perhaps a simple dropdown menu in the navigation bar—where users can select prompts for different purposes. For example:

• Create a custom forecaster/classifier/transformer/etc.
• Detail a forecasting problem and get a recommended baseline implemented.
• ...

Not all of these need to be implemented immediately. A good starting point would be the first one, since the extension templates are especially useful for that. We should also consider whether it’s possible, using Sphinx, to automate the updating of such prompts when the underlying source code changes. In other words, if someone updates an extension template file or any other referenced source code, the corresponding prompt in the documentation should be updated automatically during the documentation build process.

Suggest a potential alternative/fix

One alternative is to simply copy the extension templates into the documentation. However, I believe this is not enough—many users are unaware of them. Therefore, we could additionally create documentation that teaches users how to extend sktime and use these prompts effectively.