Question How to force an old GPU into task manager?

As official HD 4000 support was dropped back with Windows 8.1 you are on your own. Neither Intel nor Microsoft will be of any help in this. As long as the hardware functions it makes little difference that it appears or not.
 
Found this which may address your issue.

"Starting from June 2022, GPU is not showing on the task manager anymore even if your GPU driver is WDDM 2.0 or above, to enable GPU data in the Task Manager again, follow the steps below:

Enter Windows PowerShell in Windows Search and click on Run as Administrator:

You can also use Windows Terminal or the Command Prompt, but make sure to run it as administrator.


On PowerShell, run the following command:
lodctr /R"