### 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
#include "color_picker.h"
#include "core/input/input.h"
#include "core/io/image.h"
#include "core/math/color.h"
#include "core/os/keyboard.h"
#include "core/os/os.h"
#include "scene/gui/color_mode.h"
#include "scene/resources/image_texture.h"
#include "scene/resources/style_box_flat.h"
#include "scene/resources/style_box_texture.h"
#include "scene/theme/theme_db.h"
#include "servers/display_server.h"
#include "thirdparty/misc/ok_color.h"
#include "thirdparty/misc/ok_color_shader.h"
List<Color> ColorPicker::preset_cache;
List<Color> ColorPicker::recent_preset_cache;
void ColorPicker::_notification(int p_what) {