Acts 17:11 gets preached as a compliment about eagerness. The verb underneath it is not a compliment about eagerness. Anakrino is a legal word: to examine, to cross-examine, to sift a claim by questioning it. Luke uses the same verb in Luke 23:14 for what Pilate did to Yeshua, a Roman governor conducting a judicial examination.

Sha'ul uses it repeatedly of himself being examined. It is a small thing to me that I should be examined by you, he writes in 1 Corinthians 4:3, and my defense to those who examine me is this, in 1 Corinthians 9:3. He knew what the word meant, and he did not object to being on the receiving end of it. The Bereans were doing to him exactly what he expected to have done to him.

Set it beside the Hebrew darash, to seek, to inquire, to search out, and you have functional twins. The Bereans were not inventing a posture for a new faith. They were doing the oldest thing in their own house, and they aimed it at the emissary standing in front of them rather than at strangers.