to go out: to move from inside a place into the open, or to emerge from wherever something was held
This is the plain Aramaic verb for leaving a place. In the Aramaic chapters of Daniel it does no special religious work: it simply reports that something moved from inside to outside, and the interest always lies in what was left behind and who was watching.
What holds its shades together is a threshold. Something is inside, and then it is outside and in view. That one picture covers a captain of the guard setting off on his errand, three men walking out of a blazing furnace when the king calls them, fingers appearing against a lamplit wall, and a river of fire streaming out from a throne. The word tells you only that a boundary was crossed; the drama belongs to the scene.
An official order can cross that boundary too. When a royal decree "goes out" in Daniel 2:13, nothing physically travels. The sentence has left the king's mouth and is now in force. English keeps the same idiom, so a translation can say "the decree went out" and lose nothing.
The natural counterpart is the Aramaic verb for going in (עֲלַל), and in the court scenes of Daniel the two trade off as officials come and go before the king.