This is, in fact, the very worst place the Caliph could have chosen to stay, and is (if the players are awake) an indication of just how naive he is.
The subtle politicians of Thoqmaxar recognise the advantages of having a naive and manipulable Caliph of Agvhazar. The last thing they want to do is have him bumped off (and potentially replaced by someone more competent).
The same is true of Agvhazar's other neighbours. There are, undoubtedly, spies working for everywhere you can think of and several places you can't hanging around the Embassy. But they all have orders not to harm the Caliph.
In fact, the only people who might want to dispose of the Caliph are people involved in the internal politics of Agvhazar. And the only place you'll find such people in Thoqmaxar is inside the Embassy of the Caliphate.
Despite which, there are no assassination attempts. No-one poisons the Caliph's food at the banquet, and no-one tries to sneak into the harem (or wherever else he sleeps) overnight to stick a dagger in his back.
Which does not mean that nothing happens overnight. A lot will happen overnight. It's just that none of it directly affects the player characters yet. For a start, all those spies I mentioned just now will send reports to their assorted bosses describing the adventurers accompanying the Caliph, and asking for instructions.
And since spies mostly spy on one another, there will be a lot of spying going on in order to find out who knows what and what he/she is going to do about it. If the player characters include someone from the spying community, he/she will notice (and may be seen noticing, and possibly even approached to spy on the Caliph for someone or other), but no-one else would.