Vivenna Throws Nightblood at the Soldiers
These men in soldier uniforms, as hinted at by how they react to Nightblood, are just a bunch of Denth's mercenaries wearing uniforms to hide them. The guards at the front gates, however, are actual court guards. They don't know that insurgents are now in control of the palace; they're confused and are taking orders from Bluefingers, whom they see as someone with respect and authority.
The priests of the various gods are not so accommodating. There's mass chaos among them, though many parts of the city don't even know something strange is going on. The tunnels out of the Court of Gods are clogged with priests getting their various deities out of danger, which is why Bluefingers is slightly frustrated in the Siri scenes. He can't get the God King out to the boat he has waiting. (He wants to keep him as a prisoner. Executing him as he outlines to Siri is a backup plan, one he decides to implement.)