### Godot version

v4.0.3.stable.official [5222a99f5]

### System information

Debian 11 | Vulkan API 1.2.175 - Forward+ - Using Vulkan Device #0: NVIDIA - NVIDIA GeForce GTX 1080 | nvidia-driver 470.182.03-1 from Debian 11 | Intel(R) Core(TM) i7-8700K CPU @ 3.70GHz

### Issue description

Re-opening a scene in the editor that contains a `TextureRect` with a `ViewportTexture` and is `preload`ed in an unopened script produces the following error repeatedly and rapidly (about 200 times per second) until either the scene is closed or the script is also opened.

>ERROR: Texture (binding: 0) should provide one ID referencing a texture (IDs provided: 0).
>   at: uniform_set_create (drivers/vulkan/rendering_device_vulkan.cpp:5501)
>ERROR: Condition "!uniform_set" is true.
>   at: draw_list_bind_uniform_set (drivers/vulkan/rendering_device_vulkan.cpp:7191)
>ERROR: Uniforms were never supplied for set (3) at the time of drawing, which are required by the pipeline
>   at: draw_list_draw (drivers/vulkan/rendering_device_vulkan.cpp:7346)

### Steps to reproduce

1. Open the attached reproduction project
2. Open demo.tscn
3. Close demo.tscn
4. Open demo.tscn again

Do **not** open other.gd beforehand. Doing so will stop the problem from occurring.

### Minimal reproduction project

[reproduce_uniform_not_set.zip](https://github.com/godotengine/godot/files/11681977/reproduce_uniform_not_set.zip)

class SceneTreeTimer;
class Viewport;
class Window;
class World2D;
class ViewportTexture : public Texture2D {
	GDCLASS(ViewportTexture, Texture2D);
	NodePath path;
	friend class Viewport;
	Viewport *vp = nullptr;
	bool vp_pending = false;
	bool vp_changed = false;
	void _setup_local_to_scene(const Node *p_loc_scene);
	mutable RID proxy_ph;
	mutable RID proxy;
protected:
	static void _bind_methods();
public:
	void set_viewport_path_in_scene(const NodePath &p_path);
	NodePath get_viewport_path_in_scene() const;
	virtual void setup_local_to_scene() override;
	virtual int get_width() const override;
	virtual int get_height() const override;
	virtual Size2 get_size() const override;
	virtual RID get_rid() const override;
	virtual bool has_alpha() const override;
	virtual Ref<Image> get_image() const override;
	ViewportTexture();
	~ViewportTexture();
};
class Viewport : public Node {