Paul says that two things have happened because of "the progress of the gospel": many people inside and outside the palace have found out why he is in prison, and other Christians are no longer afraid to proclaim the good news.
Here this means fellow Christians, including both men and women, because all believers in Christ are members of one spiritual family, with God as their heavenly Father.
Paul is talking about his time in prison. AT: "that the things I suffered because I was put into prison for preaching about Jesus" (See: [[rc://en/ta/man/translate/figs-explicit]])
"Chains in Christ" here is a metonym for being in prison for the sake of Christ. "Came to light" is a metaphor for "became known." AT: "It became known that I am in prison for the sake of Christ" (See: [[rc://en/ta/man/translate/figs-metaphor]])
This can be stated in active form. AT: "the palace guards and many other people in Rome know that I am in chains for the sake of Christ" (See: [[rc://en/ta/man/translate/figs-activepassive]])
Here Paul uses the preposition "in" to mean "for the sake of." AT: "my chains for the sake of Christ" or "my chains because I teach people about Christ"
# my chains
Here the word "chains" is a metonym for imprisonment. AT: "my imprisonment" (See: [[rc://en/ta/man/translate/figs-metonymy]])