Sony has already clearly stated in its financial reports that Death Stranding 2 is a first-party game. In their interpretation, any game they have 100% financed is considered a first-party title. And that's exactly what happened with Death Stranding 2: it was fully financed by Sony, and they also provided support through the xDev team.
The fact that they don't own the IP doesn't change anything. They also don't own the IPs for Spider-Man or Wolverine, yet those are still considered first-party games.