### 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
BIND_ENUM_CONSTANT(MODE_OKHSL);
	BIND_ENUM_CONSTANT(SHAPE_HSV_RECTANGLE);
	BIND_ENUM_CONSTANT(SHAPE_HSV_WHEEL);
	BIND_ENUM_CONSTANT(SHAPE_VHS_CIRCLE);
	BIND_ENUM_CONSTANT(SHAPE_OKHSL_CIRCLE);
	BIND_ENUM_CONSTANT(SHAPE_NONE);
	BIND_THEME_ITEM_CUSTOM(Theme::DATA_TYPE_CONSTANT, ColorPicker, content_margin, "margin");
	BIND_THEME_ITEM(Theme::DATA_TYPE_CONSTANT, ColorPicker, label_width);
	BIND_THEME_ITEM(Theme::DATA_TYPE_CONSTANT, ColorPicker, sv_width);
	BIND_THEME_ITEM(Theme::DATA_TYPE_CONSTANT, ColorPicker, sv_height);
	BIND_THEME_ITEM(Theme::DATA_TYPE_CONSTANT, ColorPicker, h_width);
	BIND_THEME_ITEM(Theme::DATA_TYPE_CONSTANT, ColorPicker, center_slider_grabbers);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, screen_picker);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, expanded_arrow);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, folded_arrow);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, add_preset);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, shape_rect);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, shape_rect_wheel);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, shape_circle);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, bar_arrow);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, sample_bg);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, overbright_indicator);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, picker_cursor);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, color_hue);
	BIND_THEME_ITEM(Theme::DATA_TYPE_ICON, ColorPicker, color_okhsl_hue);
	BIND_THEME_ITEM_EXT(Theme::DATA_TYPE_STYLEBOX, ColorPicker, mode_button_normal, "tab_unselected", "TabContainer");
	BIND_THEME_ITEM_EXT(Theme::DATA_TYPE_STYLEBOX, ColorPicker, mode_button_pressed, "tab_selected", "TabContainer");
	BIND_THEME_ITEM_EXT(Theme::DATA_TYPE_STYLEBOX, ColorPicker, mode_button_hover, "tab_selected", "TabContainer");
}
ColorPicker::ColorPicker() {