Briar works via bluetooth, local wifi and internet. So internet block you can still use bluetooth and local wifi. No server needed.
Signal proxies are also available.
Discussion
I’m sorry I’m not tech savvy so this is probably a dumb question, but how could local Wi-Fi work if internet is blocked?
Same as your home network. Your pc can still talk to your phone if they are on the same wifi network. They just need internet if they are talking via a server. Briar does not use a server.
https://briarproject.org/how-it-works/
explains it better