Workaround for current Big Sur Dock Bug

What you need to do is open the dock highlight the open app that you want to add to the doc press VO + hh to get into the VoiceOver help menu then type the letters ri and press return then arrow down to options in the menu that pops up and right arrow into the sub menu and you will hear keep in dock press VO + space. Hope this helps!

Press vo plus d, choose an app, turn trackpad voiceover commands off by holding vo and performing the rotor gesture to the left, then use control plus mouse click to open the context menu and do whatever.

I hardly ever use the dock anymore. I've just gotten used to hitting Command+Shift+A to open the Applications folder and then hitting the first few letters of the app I want to focus on it. Or hitting Command+Space to pop open Spotlight and typing in the name of the app and hitting enter to launch it immediately.

And we have to be grateful to Apple for brekaing a feature that has worked for very long time and also we need to wait for very long time for a fix.

Set the VoiceOver on the element you want to add to the Dock and press CTRL + CMD + Shift + t.
All the best
Jürgen