Tooltip on a St.Bin in an extension indicator in status bar?

Desktop
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2

You can create a widget and add it to Main.layoutManager.uiGroup, then place it one the screen appropriately:

let label = new St.Label({ text: 'Tooltip' });

Main.layoutManager.uiGroup.add_child(label);
Main.layoutManager.uiGroup.set_child_above_sibling(label, null);

let [x, y] = someParentActor.get_transformed_position();
label.set_position(x, y);

Generally I’d avoid tooltips, since they aren’t very accessible and there’s other UX concerns, but that’s more or less how you would do it.