Same behavior here with latest Brave update, running on Ubuntu and also Debian. All attempts to connect end in “Make sure your computer has an active internet connection.” along with a LOG OUT button.
In Windows 11, also with latest Brave update, I am sometimes able to establish a functional connection to web.whatsapp.com after a second attempt – first attempt dies with “Make sure your computer has an active internet connection” and the LOG OUT button. Clicking that button results in a logout, followed a minute or more later of the generation of a new QR code. Scanning that new code will then usually get me in to web.whatsapp.com. Again, this semi-successful behavior only in Windows.
From what I can tell, and in all of Windows 11, Ubuntu, and Debian, this is recent behavior only seen with the latest brave update: 1.39.122
I experience no such issues with Chrome, nor generic Chromium, nor Firefox. All of them updated to latest available versions.