I was connected to WiFi, but no Internet on MacBook Pro 2013. I have been running Big Sur 11.1 successfully for a few weeks until today when I did NVRAM (or PRAM) reset to resolve the AirPods issue. I tried all solutions mentioned by OS X Daily and this thread - none of them worked (even deleting .plist files).
I have been using VPN intermittently recently. I connected back to the VPN (Windscribe). Voila! Everything started working automagically (both - with and without the VPN).
I'd love to figure out what happened behind the scenes.