def METHOD_NAME(self, value, dialect):
    """
    Process the value being bound.
    If PostgreSQL is in use, just use the string representation of the UUID.
    Otherwise, use the integer as a hex-encoded string.
    Args:
        value (object): The value that's being bound to the object.
        dialect (sqlalchemy.engine.interfaces.Dialect): The dialect in use.
    Returns:
        str: The value of the UUID as a string.
    """
    if value is None:
        return value
    elif dialect.name == "postgresql":
        return str(value)
    else:
        if not isinstance(value, uuid.UUID):
            return f"{uuid.UUID(value).int:032x}"
        else:
            # hexstring
            return f"{value.int:032x}"