### Godot version

4.0.3-stable

### System information

Windows 10

### Issue description

In some projects ViewportTexture remains pink and doesn't render viewport content after upgrading from 4.0.2-stable to 4.0.3-stable. If a pair of files viewport.h/viewport.cpp are downgraded back to what they were in 4.0.2-stable, problem goes away.

This is how it looks in 4.0.3-stable:
![4 0 3_stable_viewport_4 0 3](https://github.com/godotengine/godot/assets/1449921/44c191a9-4b67-4b02-90b6-4ab615f62a73)

And this is how it looks if viewport.h/viewport.cpp are downgraded back to what they were in 4.0.2-stable.
![4 0 3_stable_viewport_4 0 2](https://github.com/godotengine/godot/assets/1449921/f5abc605-f129-4222-9c0e-e9a07621dd9d)



### Steps to reproduce

Unfortunately, I cannot come up wit a simple demo project reproducing the problem. It exists in some projects and doesn't exist in others.


### Minimal reproduction project

Cannot produce a simple project reproducing the problem. In simple projects it works fine.
ERR_READ_THREAD_GUARD_V(false);
	return handle_input_locally;
}
void Viewport::set_default_canvas_item_texture_filter(DefaultCanvasItemTextureFilter p_filter) {
	ERR_MAIN_THREAD_GUARD;
	ERR_FAIL_INDEX(p_filter, DEFAULT_CANVAS_ITEM_TEXTURE_FILTER_MAX);
	if (default_canvas_item_texture_filter == p_filter) {
		return;
	}
	default_canvas_item_texture_filter = p_filter;
	switch (default_canvas_item_texture_filter) {
		case DEFAULT_CANVAS_ITEM_TEXTURE_FILTER_NEAREST:
			RS::get_singleton()->viewport_set_default_canvas_item_texture_filter(viewport, RS::CANVAS_ITEM_TEXTURE_FILTER_NEAREST);
			break;
		case DEFAULT_CANVAS_ITEM_TEXTURE_FILTER_LINEAR:
			RS::get_singleton()->viewport_set_default_canvas_item_texture_filter(viewport, RS::CANVAS_ITEM_TEXTURE_FILTER_LINEAR);
			break;
		case DEFAULT_CANVAS_ITEM_TEXTURE_FILTER_LINEAR_WITH_MIPMAPS:
			RS::get_singleton()->viewport_set_default_canvas_item_texture_filter(viewport, RS::CANVAS_ITEM_TEXTURE_FILTER_LINEAR_WITH_MIPMAPS);
			break;
		case DEFAULT_CANVAS_ITEM_TEXTURE_FILTER_NEAREST_WITH_MIPMAPS:
			RS::get_singleton()->viewport_set_default_canvas_item_texture_filter(viewport, RS::CANVAS_ITEM_TEXTURE_FILTER_NEAREST_WITH_MIPMAPS);
			break;
		default: {
		}
	}
}
Viewport::DefaultCanvasItemTextureFilter Viewport::get_default_canvas_item_texture_filter() const {