Hi and a belated welcome to the community.
There is a known issue that I think is related to your issue. Posting information below. The linked topic is very active and you may want to look it over. Ditto for the Brave GitHub issue report. You may want to track both the topic and the issue report as any new updates will most likely be posted there.
Hope this helps! Please post an update. Take care. 
ISSUE: Whatsapp Not Working
Workaround:
- Disasble Honey extension if installed
- Disable
Use hardware acceleration when availableatbrave://settings/system - Close and relaunch Brave
Topic Reference: Whatsapp Web is not working
Brave GitHub Issue Report (Source):
Web.whatsapp.com fails to authenticate and returns “Make sure you computer has an active internet connection”
Source: As posted in User Solutions: Brave Release 1.42.x