I’ll second this. Exact same behavior with same Brave 1.21.73 (Chromium 89.0.4389.72) version (SafeInCloud says app not running, even though it is), but Google Chrome 89.0.4389.72 works fine. SafeInCloud v. 21.0.1 extension installed in both browsers. Tried removing then reinstalling the extension in Brave, no diff.
I was running the SafeInCloud W10 21.0.4 version, but uninstalled it and installed the Win7-8 21.0.4 version (works fine on Win10), no diff-still “app not running” dialog. Also rebooted Win10 PC, no diff.
Tried (as possible) steps in SafeInCloud’s wiki, no diff. But those things would also apply if Chrome wasn’t working with SiC, but it is.
Update:
Based on comments and idea from the below threads, I Disabled Settings/Shields/Trackers & ads blocking – a big deal since that’s global, and it kind of defeats the main purpose of using Brave. After doing that, the SafeInCloud extension in Brave is again able to see & access the running SiC app.
To resolve the recently observed issue with the latest version of Brave browser, please, add @@http://localhost:19756/ in Custom filters under brave://adblock/ .