Li Qing's assigned task was to protect Qin Xiuyuan's household, while simultaneously conducting a search both above and below. The target wasn't just the few members of the Qin Family's Third Branch, but every possible suspicious account, letter, or document.
The Ministry of Justice's thinking was actually quite simple—they knew the Xuanqing Guard and Prince Shou were now "joining forces" and showing signs of seizing investigative authority over the case, which must mean there's intel they haven't gotten hold of yet. Most likely, this information was handed to the Xuanqing Guard by Prince Shou. Otherwise, the Xuanqing Guard, who always kept its distance from every prince, would never suddenly team up with him.
