```ts
/**
 * Flattens a deeply nested array up to a specified depth.
 * @param items - The array to flatten.
 * @param depth - The maximum depth to flatten. Defaults to Infinity.
 * @returns A new flattened array.
 */
export function flatten(items: readonly unknown[], depth?: number): unknown[] {
    if (depth === undefined) depth = Infinity;
    if (!Number.isInteger(depth) || depth < 0 && depth !== Infinity) {
        throw new Error('Depth must be a non-negative integer or Infinity');
    }

    return items.reduce((acc, item) => {
        if (Array.isArray(item) && depth > 0) {
            acc.push(...flatten(item, depth - 1));
        } else if (typeof item !== 'string') {
            acc.push(item);
        }
        return acc;
    }, [] as unknown[]);
}
```