"Use Mobile data": how about paid WiFi Connections?
In the manual there is a paragraph:
Use Mobile Data
You can control whether Briar uses mobile data. If you turn off mobile data, Briar will only use the internet when you're connected to Wi-Fi.
How about paid WiFi Connections? Android or least LineageOS distinguishes between WiFi free of charge and paid ones (translated from the german UI). Imho the Android download manager downloads if the phone is connected to a free of charge WiFi.