As someone who does a fair bit of writing, one of the features of the Bible that most persuades me of its authenticity is the staunch refusal of its writers to satisfy our curiosity about details.
An authentic historical account written for people familiar with the relevant culture and events naturally leaves out all sorts of facts its original audience would be expected to already know and understand. It cuts directly to the chase. This is what we find in scripture’s books of history. Likewise, an authentic letter does not read like a narrative or polemic conveniently disguised in another literary form. It is not an info dump. It is marked as much by what it doesn’t include as by what it does.
In short, each genre of scripture reads just as we might expect it to. Philemon is a fine example of this.