### 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(Size2());
	return _get_size();
}
void SubViewport::set_size_2d_override(const Size2i &p_size) {
	ERR_MAIN_THREAD_GUARD;
	_set_size(_get_size(), p_size, true);
}
Size2i SubViewport::get_size_2d_override() const {
	ERR_READ_THREAD_GUARD_V(Size2i());
	return _get_size_2d_override();
}
void SubViewport::set_size_2d_override_stretch(bool p_enable) {
	ERR_MAIN_THREAD_GUARD;
	if (p_enable == size_2d_override_stretch) {
		return;
	}
	size_2d_override_stretch = p_enable;
	_set_size(_get_size(), _get_size_2d_override(), true);
}
bool SubViewport::is_size_2d_override_stretch_enabled() const {