"""Transforms a JSON Schema from MCP format into Harmony's variant.

This function processes a given JSON Schema dictionary to conform to Harmony's specific requirements. It performs the following transformations:
1. Removes the 'title' key if present.
2. Removes the 'default' key if its value is None.
3. Converts the 'anyOf' key into a 'type' key, combining the types from the 'anyOf' array while excluding the 'null' type.
4. Recursively processes nested 'properties' to apply the same transformations.

Args:
    schema (dict): The JSON Schema dictionary to be transformed.

Returns:
    dict: The transformed JSON Schema dictionary conforming to Harmony's variant.
"""
You should write code starting with:
from typing import Dict, Any

def trim_schema(schema: Dict[str, Any]) -> Dict[str, Any]:
    pass

