There is a setting in the mod settings to remove the menu button if it doesn't look nice in the mod menu.
That was the exact reason I added the setting to remove it. I also find it annoying if there are some unnecessary buttons there.
Once removed you can always right click on the planner instead to open the menu.
I do find it odd that GUI Unifyer doesn't change my button along with the others. It's literally created using mod_gui.get_flow_button(). And then literally adding a sprite button to it with the mod_gui.button style.
You'd expect that something called GUI Unifyer can catch the most base case instead of having to add mod support manually for each mod.