```python
def format_bits(value: int, width: int) -> str:
    """
    Render value as unsigned binary in exactly width bits: most significant bit first,
    left-padded with zeros to the full width, and split into groups of four bits joined by single spaces.
    Reject a value that is not a non-negative integer, a width that is not a positive multiple of four or exceeds 32,
    and a value that does not fit in width bits, with an error.
    """
    if not isinstance(value, int) or value < 0:
        raise ValueError("Value must be a non-negative integer.")
    
    if not (isinstance(width, int) and width > 0 and width % 4 == 0 and width <= 32):
        raise ValueError("Width must be a positive multiple of four and no more than 32 bits.")
    
    binary_str = bin(value)[2:]  # Convert to binary string without '0b' prefix
    if len(binary_str) > width:
        raise ValueError(f"Value {value} does not fit in {width} bits.")
    
    padded_binary_str = binary_str.zfill(width)
    formatted_bits = ' '.join(padded_binary_str[i:i+4] for i in range(0, width, 4))
    
    return formatted_bits
```