"Given this opportunity, I guess the public performance will be replaced by a more exclusive one. Let's create the story of Gilgamech's fall."

Leokoris follows Darbakh steps behind, visibly smiling to the mere thought of what's to come.

On the other side of the door is a grand office. In the middle is a large desk stacked with countless papers.

I rifle through the papers, looking for anything incriminating on Gilgamech.

There isn't anything incriminating so to speak, but as you search you accidentally activate something and a small hidden drawer springs out, containing several letter envelopes.
They are all addressed to Gilgamech, but there is nothing saying who they are from.
The first letter seems to b a quarterly report. But it's clear right off the bat that no-one is supposed to see the source of any of the gold.
All names an locations are scribbled out, as well as several numbers.
You are still holding the the letter when you hear the door handle start to turn.

Shi-

If there’s a window in the room, I’ll cast misty step (bonus action) and teleport outside. Alternatively, since Leokoris and Darkbakh would still be there, I could try casting charm person on the person. (depends on what they do)

Leokoris founds odd that such precautions were taken to hide this report, destroying it would have been way easier for them. Maybe they still wanted to keep a track of the information for their own usage ?

When he hears the door handle starting to move, he grabs his lute, trying to appear as if he was looking for Gilgamech with the intend to make a performance for him.

Darbakh attempts to simply hide behind the desk, as he has neither the persuasive charm nor the alibi the other two do.

So, one of you exits the room through the window, one pretends to be looking for Gilgamech, and on hides under the desk with indeed has a front.
The door opens and the man himself enters. Upon seeing Leokoris, he freezes for half a second before ringing a bell on the wall that doesn't make any noise.
"Well, what have here?The party my friend, is out there." He gestures to the other side of the door.
Under the desk, Darbakh feels the talk stone vibrating in his pocket.
Grammy was trying to make contact.
Gilgamech strides closer to the desk. Leo (is that alright) sees his eyes flicker to the drawer and papers that nobody did anything with, but he doesn't mention them.
"Security is on the way. They will ask you questions.
If you value your head, you'll answer them truthfully."
With that he leans over to close the drawer, putting the papers back in before leaving to join the party again.