### 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
btn_preset = memnew(Button);
	btn_preset->set_text("Swatches");
	btn_preset->set_flat(true);
	btn_preset->set_toggle_mode(true);
	btn_preset->set_focus_mode(FOCUS_NONE);
	btn_preset->set_text_alignment(HORIZONTAL_ALIGNMENT_LEFT);
	btn_preset->connect("toggled", callable_mp(this, &ColorPicker::_show_hide_preset).bind(btn_preset, preset_container));
	real_vbox->add_child(btn_preset);
	real_vbox->add_child(preset_container);
	recent_preset_hbc = memnew(HBoxContainer);
	recent_preset_hbc->set_v_size_flags(SIZE_SHRINK_BEGIN);
	recent_preset_hbc->hide();
	recent_preset_group.instantiate();
	btn_recent_preset = memnew(Button);
	btn_recent_preset->set_text("Recent Colors");
	btn_recent_preset->set_flat(true);
	btn_recent_preset->set_toggle_mode(true);
	btn_recent_preset->set_focus_mode(FOCUS_NONE);
	btn_recent_preset->set_text_alignment(HORIZONTAL_ALIGNMENT_LEFT);
	btn_recent_preset->connect("toggled", callable_mp(this, &ColorPicker::_show_hide_preset).bind(btn_recent_preset, recent_preset_hbc));
	real_vbox->add_child(btn_recent_preset);
	real_vbox->add_child(recent_preset_hbc);
	set_pick_color(Color(1, 1, 1));
	btn_add_preset = memnew(Button);
	btn_add_preset->set_icon_alignment(HORIZONTAL_ALIGNMENT_CENTER);
	btn_add_preset->set_tooltip_text(RTR("Add current color as a preset."));
	btn_add_preset->connect("pressed", callable_mp(this, &ColorPicker::_add_preset_pressed));
	preset_container->add_child(btn_add_preset);
}
ColorPicker::~ColorPicker() {