Merge Closed Intervals

Question

Given a list of closed intervals `[start, end]`, merge every overlapping pair and return the resulting non-overlapping intervals sorted by start position.

```python
def merge_intervals(intervals: list[list[int]]) -> list[list[int]]: ...
```

Assume `start <= end`. Because intervals are closed, `[1, 4]` and `[4, 6]` overlap and become `[1, 6]`. The input may be unsorted and may contain duplicates.

## Staged follow-ups

1. Preserve associated metadata while merging.
2. Insert one interval into an already sorted, disjoint sequence.
3. Process intervals that arrive as a stream and discuss when output can be finalized.