```ts
/**
 * Walks a courier relay directory station by station.
 */

export function traceRelay(links: Record<string, string>, start: string): string[] {
  if (typeof start !== "string") {
    throw new Error("start must be a string");
  }
  if (start === "") {
    throw new Error("start cannot be an empty string");
  }
  if (!(start in links)) {
    throw new Error("unknown starting station");
  }

  const path: string[] = [];
  let current = start;

  while (true) {
    if (current === "") {
      path.push(current);
      break;
    }
    if (path.includes(current)) {
      throw new Error("relay contains a circular chain");
    }
    path.push(current);
    const next = links[current];
    if (next === "") {
      path.push(current);
      break;
    }
    if (typeof next !== "string") {
      throw new Error("link value must be a string");
    }
    if (!(next in links)) {
      throw new Error("link points to a station not in the directory");
    }
    current = next;
  }

  return path;
}
```

Key fixes:
- **Circular chain**: `path.includes(current)` check before each step detects and rejects a relay that revisits a station.
- **Broken link**: `typeof next !== "string"` rejects non-string link values; `!(next in links)` rejects links pointing to a station absent from the directory.
- **Start validation**: `typeof start !== "string"` and `start === ""` reject non-string starts and empty strings.
- **Empty string in directory**: `!(start in links)` (already present) plus the explicit `start === ""` check rejects an empty string among the directory's station names.