Little epilogue to this is that I realized when looking up the booking on Lufthansa’s own site under my fare details it clearly says Seat Reservation is included. Called back to point this out but the agent still just says it’s not and it would be chargeable.

Asked if I could speak to a supervisor and they said one would call me back in an hour. It’s been 26 hours without a callback so I’m guessing that’s not happening…