Philemon means affectionate , as its root is kiss.
Apphia could be protect one/shield or a variant of Joseph, fruitful/increasing
Archippus-great name for a soldier-master of the horse

This often gets pushed aside but has a number of ways to make a sermon or a good study.

First Philemon is a slaveholder and Onesimus (useful) is a slave. If one is a storyteller, the opening here would be for background, especially on how Onesimus meets up with Paul in the first lace.

AT v. 7 hearts="gut" as in gut wrenching, or deeply moved.
Later, Paul uses another term that is translated as my own heart.

I find this a masterpiece of persuasion. I appreciate Paul's announcing that he could try to make an order but he won't (v.8). He builds the recipients up and notes the personal  gifts of grace he has received from the recipients. He is relying on the best of the slaveholder. Paul aims for sympathy due to his age and condition as a prisoner. He wants Philemon to make a decision and not be presented with a fait accompli of Paul's holding on to Onesimus.

Notice how careful he is with words. Onesimus has been separated from his master-think of the words he could have used (v. 15). He wants a welcome fit for Paul himself for this returning member of the economic  realm.
Look at how he turns reciprocity language-Philemon owes Paul his own self, but Paul will repay from his own account

I am moved to despair when I read Christians on social media. They assume that they are in the absolute right and opponents are absolutely wrong. They call people terrible names. They do not seek to try to see things from another point of view.

Social sin seems to bring out the jeremiad in ministers, even when they will not speak that way about personal sin often.

Should Christians align with identity politics as antithetical to the  beloved community?

This letter is the personal as political, but Paul makes no grand political statements her. except for his constant reference to the new community in Christ.