macOS 11 Big Sur has a bug that prevents some apps from appearing in the "Default web browser" menu in the General pane of System Preferences, which makes it difficult to set one of those apps as your default web browser. My own Link Unshortener is affected, among many others. I blogged about this bug two months ago. I'm told that the bug still exists in the latest 11.3 beta versions, unfortunately, so I'm pessimistic about the prospects of a fix coming from Apple. Therefore, I've decided to take matters into my own hands and write an app to change your default web browser on Big Sur. This new app is named "Default web browser". (There are only two hard things in computer science: changing your default web browser and naming things.)
Default web browser is free and open source. You can download the app now from GitHub. Default web browser is a Universal Binary for Intel and Apple Silicon Macs, and it requires macOS 11 Big Sur. You don't need the app on Catalina and earlier, because System Preferences works as expected there.
I just threw together Default web browser today in a few hours, so I haven't (yet) created an app icon. (Ok, there are three hard things in computer science.) Hopefully you shouldn't have to run the app too often anyway. Indeed, hopefully Apple will render this app obsolete within a few months, by fixing their bug. But if not, then enjoy the free app!