The coronation was already scheduled.
The Dark Cult only wanted the Empire of Ataraxia for the Sacred Chains, sure, but they still had to take care of the nation. The Third Prince had to ascend to the throne to give the people peace of mind.
When they had peace of mind, they would be less curious about what was happening under their noses. In the peace, they would be unaware that they were only days away from becoming sacrifices to the Great Demon God.
In three days, the Third Prince would rise to the throne and become the Emperor. The Second Prince would be executed, and the empire would regain its majesty.
That was the narrative they pushed, but how could it be true?
With the empire under their total control, they could take all the time they needed to torture the Emperor and learn the location of the Sacred Chains. Everything else could progress from there.
'However, this nation cannot be ruined until we have taken the Sacred Chains.'