```ts
/**
 * Merge overlapping intervals into non-overlapping ones, sorted by start.
 * @param intervals - List of [start, end] pairs to merge.
 * @returns A new list of merged [start, end] pairs, sorted ascending 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 merged: number[][] = [sortedIntervals[0]];

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

    if (current[0] > current[1]) throw new Error('Invalid interval: start must be <= end');

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

  return merged;
}
```