Luxury clothing houses have long valued direct personal interaction through their boutiques and fashion shows. Perusing the sumptuous goods in a shop, with a glass of champagne in hand, promises a superior consumer experience to the mundane act of ordering online, and sitting front row at a catwalk remains a coveted status symbol. That’s why there’s more on display than the latest looks at the September fashion weeks that are getting under way in London, Milan and Paris. This year, they’re a proving ground for just how successfully the industry has reinvented itself for the age of social distancing to push its message and products through digital channels. Burberry Group Plc’s show on Sept. 17 provided a snapshot of the challenges that await. A walk-up segment featured celebrities including supermodel Bella Hadid and soul artist Erykah Badu engaged in a halting…