I think a possible solution to dragging tabs out of the tab-area would be to simply use an overlay that appears only when dragging outside.
When dragging a tab inside the tab-area, it should drag the actual tab. However, when dragging outside, it should switch to dragging an overlay and just leave the real tab. This way, we should be able to avoid the issue of the tab getting clipped.
That could probably be a solution š¤