### Godot version

v4.1.dev.custom_build [18112ba36]

### System information

Linux Mint 21.1, NVIDIA GeForce GTX 1050 Ti,  Vulkan API 1.3.205

### Issue description

This is a regression from #64388. 

Textures seem to be used differently in 2D and 3D. They are rendered using the `RID` in 3D, and changing the `viewport_path` will cause the `RID` to change.

https://github.com/godotengine/godot/assets/30386067/ad393fe8-50c1-4a89-870d-58d4e224bcc6


### Steps to reproduce

1. Download and import MRP.
2. Open 1.tscn, and try to switch the `viewport_path` of the `MeshInstance3D:mesh:material:albedo_texture` in the MeshInstance3D node.
3. After switching, the MeshInstance3D is rendered as white in the editor;
4. Close and then reopen 1.tscn.

### Minimal reproduction project

[ViewportTexture-change-viewport_path.zip](https://github.com/godotengine/godot/files/11509010/ViewportTexture-change-viewport_path.zip)

ERR_READ_THREAD_GUARD_V(0);
	return positional_shadow_atlas_size;
}
void Viewport::set_positional_shadow_atlas_16_bits(bool p_16_bits) {
	ERR_MAIN_THREAD_GUARD;
	if (positional_shadow_atlas_16_bits == p_16_bits) {
		return;
	}
	positional_shadow_atlas_16_bits = p_16_bits;
	RS::get_singleton()->viewport_set_positional_shadow_atlas_size(viewport, positional_shadow_atlas_size, positional_shadow_atlas_16_bits);
}
bool Viewport::get_positional_shadow_atlas_16_bits() const {
	ERR_READ_THREAD_GUARD_V(false);
	return positional_shadow_atlas_16_bits;
}
void Viewport::set_positional_shadow_atlas_quadrant_subdiv(int p_quadrant, PositionalShadowAtlasQuadrantSubdiv p_subdiv) {
	ERR_MAIN_THREAD_GUARD;
	ERR_FAIL_INDEX(p_quadrant, 4);
	ERR_FAIL_INDEX(p_subdiv, SHADOW_ATLAS_QUADRANT_SUBDIV_MAX);
	if (positional_shadow_atlas_quadrant_subdiv[p_quadrant] == p_subdiv) {
		return;
	}
	positional_shadow_atlas_quadrant_subdiv[p_quadrant] = p_subdiv;
	static const int subdiv[SHADOW_ATLAS_QUADRANT_SUBDIV_MAX] = { 0, 1, 4, 16, 64, 256, 1024 };
	RS::get_singleton()->viewport_set_positional_shadow_atlas_quadrant_subdivision(viewport, p_quadrant, subdiv[p_subdiv]);
}
Viewport::PositionalShadowAtlasQuadrantSubdiv Viewport::get_positional_shadow_atlas_quadrant_subdiv(int p_quadrant) const {