I own a Surface Book 3 and am having the same issue, I can only use my Logitech Brio with Windows Hello if my laptop is open. I'm not sure if this is an example of a complete misunderstanding of a use case, or a glaring oversight of Surface users. I'm not walking around with a Logitech Brio and a USB cable using an external IR camera at the coffee shop with my laptop open. If I need to use an external camera it's almost certainly because I'm docked at home, and if I'm docked, the laptop is closed!!!
C'mon Microsoft. You made an "update" that is completely useless for every single docked Surface owner. The Surface Book is a premium product and I certainly paid a PREMIUM price for it. Please fix this and do it properly, NOW!