Who does Caesar brag to in Act III, scene 1 of "Julius Caesar"?
Concerning your question about Shakespeare's Julius Caesar, Caesar brags to numerous people in Act 3.1, though he brags to them all at the same time.
The list of who is present is at the beginning of the act. They are, presumably, all still present, listening to Caesar's words when he demonstrates a bit of arrogance.
Metellus is about to ask Caesar for mercy concerning his brother, when Caesar rejects his attentions and refuses to change his mind concerning the brother. Brutus even gets involved, but Caesar is adamant. Eventually, he brags:
I could be well moved, if I were as you;
If I could pray to move, prayers would move me;
But I am constant as the Northern Star. (Act 3.1.58-60)
Caesar then describes the stars, and says there is but one that cannot be moved, and compares himself to that one:
Yet in the number I do know but one
That unassailable holds on his rank.
Unshaked of motion: and that I am he,
Let me a little show it, even in this--
That I was constant. Cimber should be banished.
And constant do remain to keep him so. (Act 3.1.68-73)
Caesar will not be swayed. Of course, soon, he will be dead.