There is little more to tell. A bishop from the Church with known Rebel sympathies (it might be more accurate to say that he is more aware of which way the wind is blowing than most of the church) verifies that yes, this is the true crown, and yes, he is willing to perform the ceremony to mark Freddie as the Vessel of the Divine in a sufficiently public place that the Church won’t be able to deny it. This happens. It sparks a public brawl between those who think Freddie should be lynched, and those who think that lynching the Vessel for the Divine is blasphemy. Freddie flees, fakes boarding a train to Arakesh, and sneaks away.
The party sneak their way up into the Imperial Spire itself. It’s quiet. Most of the guards have been posted on the streets to try and contain the rioting; when they find the Dauphin, he is alone in his room watching the darkened Seflheim. The party are expecting a battle, or some sort of resistance, but in the end he’s just one man. They incapacitate him before he can activate his magitech protection, and — after a very brief interrogation — kill him and hurl him out of a window, thenflee to Arakesh.
The Emperor is dead, and there’s no obvious line of succession. Freddie has been crowned as Vessel for the Divine. Zaszperezal is gone: fled, or in hiding; it’s not clear. The Empire, as a nation, is finished.
What will come after, of course, is yet to be seen.