Android - Why I can't scan the WhatsApp QR?
SOLUTION
Okay, first of all - you have to scan the QR-Code with the scanner that is built in WhatsApp. Not with some 3rd-party scanner-app. Click on "Whatsapp Web", then the scanner opens immediately.
BUT - apparently there is a problem with devices that have a display smaller than 4 inches!
Like with my Sony Xperia Go (3,5 inches), I can't tap on the "OK, got it"-button to make the instructions of the built-in-scanner go away.
That's it. They will have to solve this problem in a later version, I guess.
Turn off WiFi.
Apparently, WhatsApp only connects itself to the web session if it's online via mobile data.
To repeat a comment by Almir Campos that solved my issue: If your browser has an extension such as Dark Reader which makes pages night-themed and inverts the color of the QR code, WhatsApp won't be able to scan it. Make sure you disable any color-inverting extensions or settings on web.whatsapp.com before scanning the QR code.