### 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
shader_type canvas_item;
void fragment() {
	float x = UV.x - 0.5;
	float y = UV.y - 0.5;
	float a = atan(y, x);
	x += 0.001;
	y += 0.001;
	float b = float(sqrt(x * x + y * y) < 0.5) * float(sqrt(x * x + y * y) > 0.42);
	x -= 0.002;
	float b2 = float(sqrt(x * x + y * y) < 0.5) * float(sqrt(x * x + y * y) > 0.42);
	y -= 0.002;
	float b3 = float(sqrt(x * x + y * y) < 0.5) * float(sqrt(x * x + y * y) > 0.42);
	x += 0.002;
	float b4 = float(sqrt(x * x + y * y) < 0.5) * float(sqrt(x * x + y * y) > 0.42);
	COLOR = vec4(clamp((abs(fract(((a - TAU) / TAU) + vec3(3.0, 2.0, 1.0) / 3.0) * 6.0 - 3.0) - 1.0), 0.0, 1.0), (b + b2 + b3 + b4) / 4.00);
}
)");
	circle_shader.instantiate();
	circle_shader->set_code(R"(
// ColorPicker circle shader.
shader_type canvas_item;
uniform float v = 1.0;
void fragment() {
	float x = UV.x - 0.5;
	float y = UV.y - 0.5;
	float a = atan(y, x);
	x += 0.001;
	y += 0.001;
	float b = float(sqrt(x * x + y * y) < 0.5);
	x -= 0.002;