### 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
dock_slot[i]->set_current_tab(first_tab_visible);
					dock_slot[i]->set_block_signals(false);
				}
			} else {
				dock_slot[i]->hide();
			}
		}
		for (int i = 0; i < vsplits.size(); i++) {
			bool in_use = dock_slot[i * 2 + 0]->is_visible() || dock_slot[i * 2 + 1]->is_visible();
			vsplits[i]->set_visible(in_use);
		}
		right_hsplit->set_visible(right_l_vsplit->is_visible() || right_r_vsplit->is_visible());
	}
}
void EditorNode::_dock_tab_changed(int p_tab) {
	
	_update_dock_slots_visibility(true);
}
void EditorNode::_restore_floating_dock(const Dictionary &p_dock_dump, Control *p_dock, int p_slot_index) {
	WindowWrapper *wrapper = Object::cast_to<WindowWrapper>(p_dock);
	if (!wrapper) {
		_dock_make_float(p_dock, p_slot_index, false);
		wrapper = floating_docks[floating_docks.size() - 1];
	}
	wrapper->restore_window_from_saved_position(
			p_dock_dump.get("window_rect", Rect2i()),
			p_dock_dump.get("window_screen", -1),
			p_dock_dump.get("window_screen_rect", Rect2i()));
}
void EditorNode::_load_docks_from_config(Ref<ConfigFile> p_layout, const String &p_section) {