Hey there ammarfromdoha,
We understand your mouse cursor has been jumping around unexpectedly after upgrading to Big Sur. We'll be happy to help.
To begin, we'd recommend going through the steps from this page: If your Apple wireless mouse, keyboard, or trackpad isn't working with your Mac as expected
All of the steps may be helpful. However, the steps from the section "Your mouse or trackpad doesn't track as expected" are definitely important to review.
If you still experience issues, try testing with a different wired or wireless mouse to see if the issue persists. This will help us isolate if the issue is with the mouse or something else.
Let us know how that goes or if you have any questions. Cheers!