### Godot version

v4.2.dev.custom_build [c3b0a92c3]

### System information

Debian Linux X11 Xfce

### Issue description

In the following scene tree it is not possible to write anything in `LineEditB`.
![image](https://github.com/godotengine/godot/assets/6299227/ce5f696a-d86a-402f-98f7-6a762f15543e)

I would expect, that it is possible to focus `LineEditB` with a mouse click and write into it.

Regression from #58334

### Steps to reproduce

1. Load and run MRP
2. Mouse Click into the left LineEditB
3. Type Keyboard => No letters appear in the LineEditB

Variant:

1. Load and run MRP
2. Mouse Click into the right LineEditA
3. Mouse Click into the left LineEditB
4. Type Keyboard => Letters appear in LineEditA instead of LineEditB


### Minimal reproduction project

[BugKeyInputRouting.zip](https://github.com/godotengine/godot/files/11994804/BugKeyInputRouting.zip)

if (path == p_path) {
		return;
	}
	path = p_path;
	vp_changed = true;
	if (vp) {
		vp->viewport_textures.erase(this);
		vp = nullptr;
	}
	if (proxy.is_valid() && proxy_ph.is_null()) {
		proxy_ph = RS::get_singleton()->texture_2d_placeholder_create();
		RS::get_singleton()->texture_proxy_update(proxy, proxy_ph);
	}
	if (get_local_scene() && !path.is_empty()) {
		setup_local_to_scene();
	} else {
		emit_changed();
	}
}
NodePath ViewportTexture::get_viewport_path_in_scene() const {