```ts
/**
 * Merges multiple sign-in sheets into a single sorted roster of unique badge numbers.
 * @param sheets - An array of arrays, where each inner array contains integer badge numbers in non-decreasing order.
 * @returns A sorted array of unique badge numbers found across all sheets.
 */
export function spliceShifts(sheets: number[][]): number[] {
  const mergedSet = new Set<number>();

  for (const sheet of sheets) {
    for (const badge of sheet) {
      mergedSet.add(badge);
    }
  }

  const roster = Array.from(mergedSet);
  roster.sort((a, b) => a - b);

  return roster;
}
```