### 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(0);
	return mesh_lod_threshold;
}
void Viewport::set_use_occlusion_culling(bool p_use_occlusion_culling) {
	ERR_MAIN_THREAD_GUARD;
	if (use_occlusion_culling == p_use_occlusion_culling) {
		return;
	}
	use_occlusion_culling = p_use_occlusion_culling;
	RS::get_singleton()->viewport_set_use_occlusion_culling(viewport, p_use_occlusion_culling);
	notify_property_list_changed();
}
bool Viewport::is_using_occlusion_culling() const {
	ERR_READ_THREAD_GUARD_V(false);
	return use_occlusion_culling;
}
void Viewport::set_debug_draw(DebugDraw p_debug_draw) {
	ERR_MAIN_THREAD_GUARD;
	debug_draw = p_debug_draw;
	RS::get_singleton()->viewport_set_debug_draw(viewport, RS::ViewportDebugDraw(p_debug_draw));
}
Viewport::DebugDraw Viewport::get_debug_draw() const {
	ERR_READ_THREAD_GUARD_V(DEBUG_DRAW_DISABLED);
	return debug_draw;
}
int Viewport::get_render_info(RenderInfoType p_type, RenderInfo p_info) {