@pilis
I suspect a bit of software:
There is probably some realm near the bottom of the screen - where the mouse arrow tip will cause the Windows OS Taskbar to be prepared to reappear.
Then comes a threshold - an invisible - where the mouse arrow will cause the beginning, upward reappearance of the Taskbar.
In general, if we follow each of the processes involved, somewhere in that mixture, the UP/DOWN jiggle appears to be a response.
I could only guess, what settings available to you, may be used ← and I likely would not guess well.
I suggest that you try to investigate and test, in order to learn what might be the steps that fix the issue.
One thing that may help, is to find another computer display monitor, and see how it reacts.
See what you can find out, searching online for graphics settings.
When you have worn out that effort, return here and request formal Brave Support help.
You could do that now, but you would be asking Brave Support to do the investigating for you, re an issue that does not yet have a significant amount of Brave Browser users requesting help.
The more that you know, the more considerations that you study, will help you a lot, when presenting your case. You will be prepared to answer technical matters, as precisely as you can.
In my humble opinion.