Not to mention it has already used nuclear weapons, even if it hadn't, the Federation would certainly use nuclear weapons.
So it continued to pursue the Champion Marquis, initially believing that Ji Rongxinyue was inside because the maneuvers of the Champion Marquis were identical to when Ji Rongxinyue was piloting it.
The same mecha piloted by different mecha warriors would have subtle differences when executing maneuvers. The Empire has models for distinguishing Federal exceptional mecha warriors and uses them for identification.
This was one of the reasons Ji Xinghe previously managed to deceive Aida Kang, and it is also one of the reasons for Aida Kang's current frantic pursuit.