Thanks for continuing to update. My Fed35 is on Wayland and brave is on the same version as you with no issues. Odd that you have the same issue on Chrome but I suspect that doesn’t rule out issues in either direction.
As to the cursor up or down both detaching a tab to form a new window that is certainly my experience too and I have believed that to be normal behaviour.
For me the factor has always been to maintain the horizontal line of the tabs if you want to move a tab along the line, or in fact if you want to merge it back into a line, of tabs.
Hope you get to the bottom of this one as it is more than slightly intriguing
Gd luck
Just noticed there is a similar issue being talked about on this thread, might be worth a look
https://community.brave.com/t/moving-tabs-with-click-and-drag-is-not-working-anymore/323014/34