Two workarounds for this:
To move tabs left or right in a single window you can use Ctrl+Shift+PgUp and Ctrl+Shift+PgDown.
To move tabs between two Chromium windows you need to set the destination window to be "Always on top". Then dragging a tab from the source window to the destination would actually allow the tab to be inserted in the destination window, as expected.
Two workarounds for this:
To move tabs left or right in a single window you can use Ctrl+Shift+PgUp and Ctrl+Shift+PgDown.
To move tabs between two Chromium windows you need to set the destination window to be "Always on top". Then dragging a tab from the source window to the destination would actually allow the tab to be inserted in the destination window, as expected.