```ts
/**
 * Merges overlapping intervals into non-overlapping ones.
 * @param intervals - List of [start, end] pairs to merge.
 * @returns A new list of merged intervals, sorted by start.
 */
export function mergeIntervals(intervals: number[][]): number[][] {
  if (intervals.length === 0) return [];

  const sortedIntervals = intervals.slice().sort((a, b) => a[0] - b[0]);
  const result: number[][] = [sortedIntervals[0]];

  for (let i = 1; i < sortedIntervals.length; i++) {
    const current = sortedIntervals[i];
    const lastMerged = result[result.length - 1];

    if (current[0] > lastMerged[1]) {
      result.push(current);
    } else if (current[1] > lastMerged[1]) {
      result[result.length - 1] = [lastMerged[0], current[1]];
    }
  }

  return result;
}
```