(Source) Your Asiana A350 ride.
On the same plane the economy seats don't have that shoulder strap. It's not new either. There are various reasons:
- Most business class seats are not forward facing. For your ride it's a slight angle but it's there.
- It allows* reclining the seat during taxi, takeoff, and landing.
[Qantas will] offer the world’s first seats that let passengers recline in their seat from take-off through to landing. Key to the break-through product’s safety is an over-the-shoulder belt.
- It protects the head from hitting the seat walls.
- It protects the head since there is no cushion (the knee-breaking seat in front of you in economy).
(...) the three point seat restraint is used in the larger premium class seat, because there is no seat back close enough to the traveler to cushion his/her head in a sudden stop.
- It will keep you in place during turbulence when the seat is reclined.
On the return flight aboard Korean, based on flightaware it was probably a 777-300ER or a 747-8. The missing shoulder strap could be because the seats are forward facing on both types, and/or Korean wasn't interested in the option to recline during takeoff/landing.
* Allows, but not necessarily allowed by the airline, i.e., some airlines may still insist on the upright position for the takeoff/landing.
I also found this supporting text:
9.20.3 Three-point Seatbelts
Three-point diagonal fixing seatbelts are occasionally installed in premium seats, including those positioned at an angle away from the forward/aft axis of the aircraft. The intent of the three-point harness is to protect the occupant from contact with the forward side of the seat shell.
— IATA Cabin Operations Safety Best Practices Guide (skybrary.aero).