```python
def team_headcount(chart: dict, name: str) -> int:
    """Calculate the total number of workers in the team including the leader."""
    if not isinstance(chart, dict):
        raise ValueError("chart must be a mapping")
    if not isinstance(name, str):
        raise ValueError("name must be a string")
    if name not in chart:
        raise ValueError("name is not a key in the chart")

    reports = chart[name]
    if not isinstance(reports, list):
        raise ValueError("reports must be a list")

    # Validate that all reports are strings
    for report in reports:
        if not isinstance(report, str):
            raise ValueError("each report must be a string")

    # Use BFS/DFS to count all descendants.
    # We need to handle potential cycles or complex structures, but the problem
    # implies a tree or DAG structure where every report is also a key.
    # Since we need to count unique individuals, we track visited nodes.
    
    stack = list(reports)
    visited = set(reports)
    count = 1  # Start with the leader themselves
    
    while stack:
        current = stack.pop()
        # If the current person is in the chart, add their reports to the stack
        if current in chart:
            for subordinate in chart[current]:
                if subordinate not in visited:
                    visited.add(subordinate)
                    stack.append(subordinate)
                    count += 1
    
    return count
```