### 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)

} break;
		case NOTIFICATION_VP_MOUSE_EXIT: {
			gui.mouse_in_viewport = false;
			_drop_physics_mouseover();
			_drop_mouse_over();
			_gui_cancel_tooltip();
			
			
			
		} break;
		case NOTIFICATION_WM_WINDOW_FOCUS_OUT: {
			_gui_cancel_tooltip();
			_drop_physics_mouseover();
			if (gui.mouse_focus && !gui.forced_mouse_focus) {
				_drop_mouse_focus();
			}
			
			
			
			
		} break;
		case NOTIFICATION_PREDELETE: {
			if (gui_parent) {
				gui_parent->gui.tooltip_popup = nullptr;
				gui_parent->gui.tooltip_label = nullptr;
			}
		} break;
	}
}
void Viewport::_process_picking() {