You may be using the default launcher that came with your phone, but if you don’t have the search bar, then it’s still a 3rd party launcher. Google’s launcher forces an immovable search bar on to your home screen.
-Edit-
It’s possible this has changed in the years I’ve been using an alternate launcher. It’s been several years since I switched and never really checked back to see if it was still true.
You may be using the default launcher that came with your phone, but if you don’t have the search bar, then it’s still a 3rd party launcher. Google’s launcher forces an immovable search bar on to your home screen.
-Edit-
It’s possible this has changed in the years I’ve been using an alternate launcher. It’s been several years since I switched and never really checked back to see if it was still true.