Acts 16
35 And when it was day, the magistrates sent the [e]officers, saying, “Let those men go.”

36 So the keeper of the prison reported these words to Paul, saying, “The magistrates have sent to let you go. Now therefore depart, and go in peace.”

37 But Paul said to them, “They have beaten us openly, uncondemned Romans, and have thrown us into prison. And now do they put us out secretly? No indeed! Let them come themselves and get us out.”

38 And the officers told these words to the magistrates, and they were afraid when they heard that they were Romans. 39 Then they came and pleaded with them and brought them out, and asked them to depart from the city. 40 So they went out of the prison and entered the house of Lydia; and when they had seen the brethren, they encouraged them and departed.

This scripture is almost a precursor to what will happen in Chapter 22.
Minus foreshadowing it is hard for me to find a lot of purpose here. I think Paul was very proud of his Roman citizenship, OR he knew that it had a lot of importance at he loved to utilize it. Either way it will be paramount later on in the scripture.