```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;
  const bound = Object.keys(links).length;
  for (let step = 0; step < bound; step++) {
    path.push(current);
    const next = links[current];
    if (next === "") {
      return path;
    }
    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");
    }
    if (path.includes(current)) {
      throw new Error("relay contains a circular chain");
    }
    current = next;
  }
  return path;
}
```

Key fixes applied:
1. **Rejects `start` that is not a string** — `typeof start !== "string"`.
2. **Rejects empty string as a station name** — `start === ""`.
3. **Rejects a link value that is not a string** — `typeof next !== "string"`.
4. **Rejects a link to a station absent from the directory** — `!(next in links)`.
5. **Rejects a circular chain** — `path.includes(current)` check before advancing.
6. **Uses `===` for all string comparisons** (no string-to-number coercion).
7. **Uses `in` operator** for membership checks (handles `null`/`undefined` keys correctly).