IIRC it‘s just that such a through ticketed bus service needs a sponsoring TOC to appear on displays. (It’s little different to the Isle of Wight ferries that appear on RTT for Portsmouth Harbour and are apparently operated by SW.)
Yeah I wasn't sure of the ins and outs so thank you for the little added bit. I was just correcting that LNER don't actually run a bus there and as you say just one of those quirks