Firefox works just fine.
Two browser windows, one on each monitor, multiple tabs opened on both. When dragging a tab to another, on chromium browsers it just does nothing. In firefox it does.
Within a single monitor it works.
bspwm version: 0.9.7-10-g2ffd9c1
chromium version: chromium-80.0.3987.163
brave version: Brave Browser 80.1.5.122
firefox version: Mozilla Firefox 74.0.1
(freshest everything on arch)
fwiw, it is also impossible to drag a chromium tab at all across the monitor border, i.e. to move it to a new window on the other monitor. (which works for firefox)
I have also noticed that the cursor changes to a special drag-and-drop cursor when dragging firefox tabs whereas it doesn't for chromium tabs:

Also, chromium creates a new window as soon as the cursor drag leaves the tab bar, and deletes the new window as soon as the drag enters the tab bar again, which makes dragging a tab to a new window not very usable with tabbed windows. Firefox otoh, only creates a new window when you release the mouse button.

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fwiw, it is also impossible to drag a chromium tab at all across the monitor border, i.e. to move it to a new window on the other monitor. (which works for firefox)
I have also noticed that the cursor changes to a special drag-and-drop cursor when dragging firefox tabs whereas it doesn't for chromium tabs:
Also, chromium creates a new window as soon as the cursor drag leaves the tab bar, and deletes the new window as soon as the drag enters the tab bar again, which makes dragging a tab to a new window not very usable with tabbed windows. Firefox otoh, only creates a new window when you release the mouse button.