### 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
slider_gc->set_columns(3);
	for (int i = 0; i < SLIDER_COUNT + 1; i++) {
		create_slider(slider_gc, i);
	}
	alpha_label->set_text("A");
	hex_hbc = memnew(HBoxContainer);
	hex_hbc->set_alignment(ALIGNMENT_BEGIN);
	vbr->add_child(hex_hbc);
	hex_hbc->add_child(memnew(Label("Hex")));
	text_type = memnew(Button);
	hex_hbc->add_child(text_type);
	text_type->set_text("#");
	text_type->set_tooltip_text(RTR("Switch between hexadecimal and code values."));
	if (Engine::get_singleton()->is_editor_hint()) {
		text_type->connect("pressed", callable_mp(this, &ColorPicker::_text_type_toggled));
	} else {
		text_type->set_flat(true);
		text_type->set_mouse_filter(MOUSE_FILTER_IGNORE);
	}
	c_text = memnew(LineEdit);
	hex_hbc->add_child(c_text);
	c_text->set_h_size_flags(SIZE_EXPAND_FILL);
	c_text->set_select_all_on_focus(true);
	c_text->set_tooltip_text(RTR("Enter a hex code (\"#ff0000\") or named color (\"red\")."));
	c_text->set_placeholder(RTR("Hex code or named color"));
	c_text->connect("text_submitted", callable_mp(this, &ColorPicker::_html_submitted));
	c_text->connect("text_changed", callable_mp(this, &ColorPicker::_text_changed));
	c_text->connect("focus_exited", callable_mp(this, &ColorPicker::_html_focus_exit));
	wheel_edit = memnew(AspectRatioContainer);
	wheel_edit->set_h_size_flags(SIZE_EXPAND_FILL);