This is an open letter to Facebook because their feedback system is very limited (no room for detail) and I’d rather have a public place I can link to with full details. If you work for Facebook, please tell me who I can talk to that has the power to change infrastructure details like this. If you don’t work for Facebook but know a good place I can share this important information, please point me in the right direction.
EDIT: In the end I DID find the correct place to post a technical bug to Facebook, and created a ticket about this problem with the empty user agents. I got a decent reply from them where they accepted that the problem is real and stated their intention to fix it in February 2017. As of August 2017, they claim to have fixed the problem, but unfortunately I was able to find more examples of the problem in my logs after they closed the ticket as fixed. Hopefully it will start working soon, and I’ll update this again. Below is the original post, which assumes the problem persists.