The Imperium have psionic assets too.
I'm sure that if the Imperium sent a team of psionically trained PCs into the Consulate they would find stuff out.
Very true, but the Consulate is likely holding knowledge of the Wave very close to the vest. They don't want the Proles to panic, after all.
Should the Imperium send a psi team into the Consulate, anyone with this information that a telepath could read casually would be shielded. Intell assets in the Consulate would have to be VERY careful. They believe that the Zho's are leaps and bounds ahead of them in psionic skill [remember, they don't know the Psionic Powers chapter of the rule book

] and they know for sure that everyone has a breaking point.
Now, I'm assuming that all the Cold War stuff between the West and the Soviets isn't in play. All the John le'Carre and Len Deighton novels are artifacts of their time, so while physical techniques would likely still be used [dead-drops, brush passes, etc.], much of the atmosphere and... oh, I guess 'conditions of service'... for intelligence officers aren't.
All that tells me that, while Zhodani society is more open and honest, information [especially 'doomsday' stuff] is tightly controlled. It's easy to get the easy information... finding out that a Consular Navy ship is getting ready to leave by talking to dockworkers, economic intelligence, etc.... a lot of the government and military information is gonna be MUCH harder because almost all that info is managed by Intendants and Nobles.
Something else to remember is that Imperium doesn't have a CIA or MI-6. All their 'professional spooks' are Naval Intelligence, IISS Intelligence, and United Armies J-2 officers. ALL these services have a vary parochial view to the intell they gather. INI sees things through a Navy lens and applies Navy solutions, Army J-2 does the same thing with Army solutions, IISS-I is an almost passive gatherer of intelligence [using the Detached Duty program as they do]. But IF there is a 'King Spook' in the Imperium, it's probably a bland, ignorable viscount with a small staff that collates information for the Emperor... a 'Walsingham' type figure, 'His Imperial Majesty's Doer of Very Bad Things'.
But there is no dedicated ministry that gets intell from all sources with agents everywhere, wiretaps on everything, and a titanic budget. No, not even the Office of Calendar Compliance is that big. There is no Imperial counterpart to the Tozjabr.
At least, not in canon anyway.