Correct take. "Wife's son" taken genuinely gives off very strong distancing vibes. It feels like he's trying to disown or reject his relationship to the stepson. It's kind of like when people say "baby mama" to refer to their current partner. No, there's no direct link between them and myself: we're just related by this other secondary relationship.

"my wife's _" is such a huge meme that it feels forced to even try reading it genuinely when a more organic way of wording it is available.