### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
bottom_panel->add_theme_style_override("panel", theme->get_stylebox(SNAME("BottomPanelDebuggerOverride"), EditorStringName(EditorStyles)));
		} else {
			bottom_panel->add_theme_style_override("panel", theme->get_stylebox(SNAME("BottomPanel"), EditorStringName(EditorStyles)));
		}
		center_split->set_dragger_visibility(SplitContainer::DRAGGER_VISIBLE);
		center_split->set_collapsed(false);
		if (bottom_panel_raise->is_pressed()) {
			top_split->hide();
		}
		bottom_panel_raise->show();
	} else {
		bottom_panel->add_theme_style_override("panel", theme->get_stylebox(SNAME("BottomPanel"), EditorStringName(EditorStyles)));
		bottom_panel_items[p_idx].button->set_pressed(false);
		bottom_panel_items[p_idx].control->set_visible(false);
		center_split->set_dragger_visibility(SplitContainer::DRAGGER_HIDDEN);
		center_split->set_collapsed(true);
		bottom_panel_raise->hide();
		if (bottom_panel_raise->is_pressed()) {
			top_split->show();
		}
	}
}
void EditorNode::set_docks_visible(bool p_show) {
	docks_visible = p_show;
	_update_dock_slots_visibility(true);
}
bool EditorNode::get_docks_visible() const {
	return docks_visible;
}
void EditorNode::_toggle_distraction_free_mode() {