“Now I want you to know, brothers and sisters, that my circumstances have turned out for the greater progress of the gospel, so that my imprisonment in the cause of Christ has become well known throughout the praetorian guard and to everyone else, and that most of the brothers and sisters, trusting in the Lord because of my imprisonment, have far more courage to speak the word of God without fear.” – Philippians 1:12-14 NASB2020

My thought process was that a good chunk of this was probably from the comfort of seeing how calm and collected and at peace Paul was in the midst of an imprisoned reality. People are scared of the worst case scenario. Imprisonment for the Gospel is pretty much one of them. If they were able to see a man so content and joyful in Christ in the midst of their worst case scenario for preaching the Gospel, then that must have been something really encouraging for them and made their worse fears something not really all that worrisome but something possible to overcome.