### 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 (Object::cast_to<InputEventKey>(*p_event) != nullptr || Object::cast_to<InputEventShortcut>(*p_event) != nullptr || Object::cast_to<InputEventJoypadButton>(*p_event) != nullptr) {
		ERR_FAIL_COND(!is_inside_tree());
		get_tree()->_call_input_pause(shortcut_input_group, SceneTree::CALL_INPUT_TYPE_SHORTCUT_INPUT, p_event, this);
	}
	
	if (!is_input_handled()) {
		ERR_FAIL_COND(!is_inside_tree());
		get_tree()->_call_input_pause(unhandled_input_group, SceneTree::CALL_INPUT_TYPE_UNHANDLED_INPUT, p_event, this);
	}
	
	if (!is_input_handled() && (Object::cast_to<InputEventKey>(*p_event) != nullptr)) {
		ERR_FAIL_COND(!is_inside_tree());
		get_tree()->_call_input_pause(unhandled_key_input_group, SceneTree::CALL_INPUT_TYPE_UNHANDLED_KEY_INPUT, p_event, this);
	}
	if (physics_object_picking && !is_input_handled()) {
		if (Input::get_singleton()->get_mouse_mode() != Input::MOUSE_MODE_CAPTURED &&
				(Object::cast_to<InputEventMouse>(*p_event) ||
						Object::cast_to<InputEventScreenDrag>(*p_event) ||
						Object::cast_to<InputEventScreenTouch>(*p_event)
								)) {
			physics_picking_events.push_back(p_event);
			set_input_as_handled();
		}
	}
}
void Viewport::set_physics_object_picking(bool p_enable) {