```python
def apply_overrides(base: dict, overrides: list) -> dict:
    """
    Apply command-line overrides to a base configuration dictionary.

    :param base: A flat mapping of setting names to string values.
    :param overrides: A list of strings representing overrides in the format "name=value".
    :return: A new dictionary with applied overrides.
    """
    if not isinstance(overrides, list):
        raise ValueError("Overrides must be a list.")
    
    result = base.copy()
    
    for override in overrides:
        parts = override.split('=', 1)
        
        if len(parts) != 2 or '=' not in override:
            raise ValueError("Each override must be a string with exactly one equals sign.")
        
        name, value = parts
        
        if not name or not isinstance(name, str):
            raise ValueError("Override names must be non-empty strings.")
        
        if name not in base:
            raise ValueError(f"Cannot apply override for unknown setting: {name}")
        
        result[name] = value
    
    return result
```