multi_provider: validation and error handling improvements

[mshsheikh]

This PR adds defensive checks and clearer error messages to the multi provider implementation.

Summary of changes

1. Validate model name in get_model and reject None or empty values.
2. Normalize empty model parts in _get_prefix_and_model_name so inputs like "openai/" are handled as missing model name.
3. Replace raw delete on provider mapping with a check and UserError to avoid KeyError.
4. Catch ImportError for optional litellm provider import and raise a helpful UserError that explains how to resolve the issue.
5. Validate set_mapping inputs and shallow copy the provided mapping to prevent external mutation.
6. Small docstring and annotation fixes.

[seratch]

Thanks for sending this. However, the type hints for the arguments are clear, so I don't see the necessity to have these additional validation for obviously wrong data. If we do this for many parts of this SDK, it will make the internals unnecessarily complex.

[mshsheikh]

Got it, thanks for the clarification, @seratch.