[docs] Add Google-style docstrings for dspy/adapters/chat_adapter.py ChatAdapter class #9063

[azai91]

This PR adds a Google-style docstring for ChatAdapter class and constructor
in dspy/adapters/chat_adapter.py.

Behavior verified in IPython (returns a NEW Signature class with same fields and new instructions).
No logic changes.

Help on function __init__ in module dspy.adapters.chat_adapter:

__init__(self, callbacks=None, use_native_function_calling: bool = False, native_response_types=None, use_json_adapter_fallback: bool = True)
    Args:
        callbacks: List of callback functions to execute during `format()` and `parse()` methods. Callbacks can be
            used for logging, monitoring, or custom processing. Defaults to None (empty list).
        use_native_function_calling: Whether to enable native function calling capabilities when the LM supports it.
            If True, the adapter will automatically configure function calling when input fields contain `dspy.Tool`
            or `list[dspy.Tool]` types. Defaults to False.
        native_response_types: List of output field types that should be handled by native LM features rather than
            adapter parsing. For example, `dspy.Citations` can be populated directly by citation APIs
            (e.g., Anthropic's citation feature). Defaults to `[Citations]`.
        use_json_adapter_fallback: Whether to automatically fallback to JSONAdapter if the ChatAdapter fails.
            If True, when an error occurs (except ContextWindowExceededError), the adapter will retry using
            JSONAdapter. Defaults to True.

Refs: #9063

[azai91]

@chenmoneygithub can you review this PR when you get the chance?

[chenmoneygithub]

Thanks for the PR!

[onel]

I was also thinking of helping with chat adapter and happy to see work has started.

@chenmoneygithub I think this is a super important module and the docs should include an example, what do you think?
I also think the other methods on the class should be documented as well.
I can help with that if needed

[chenmoneygithub]

I realized that the doc patching doesn't work well with mkdocs. Pushed a commit to just copy over the args.

Thanks again for the PR!