There are currently only 3 selections available on the Brave taskbar jump options (see supporting screenshots) and these are the Windows default jump options. The jump options that were previously available (e.g. New private window) are no longer available.
I did some digging and found this has happened on Google Chrome in the past and somebody found a solution (https://support.google.com/chrome/thread/12246911?hl=en&msgid=15133149). This solution will not work for Brave.
The reason this solution will not work for Brave (based on my further investigation) is because the Custom Destinations file (.customDestinations-ms) for Brave is missing (C:\Users%USERNAME%\AppData\Roaming\Microsoft\Windows\Recent\CustomDestinations).
There should be a Custom Destinations file in the above directory that matches the name of the directory for Brave found in the Implicit App Shortcuts folder (C:\Users%USERNAME%\AppData\Roaming\Microsoft\Internet Explorer\Quick Launch\User Pinned\ImplicitAppShortcuts).
My Brave Version:
Version 1.4.95 Chromium: 80.0.3987.122 (Official Build) (64-bit)
If you have any further questions in regards to this issue, please don’t hesitate to ask and I’ll do my best to find the answers.