Quite certainly, this, in principle, could be implemented by a Gnome Shell extension. However, unless you can develop one for yourself, you have to look among existing extensions on the Gnome Shell Extensions website. The issue is that an extension may not anymore work on your version of Gnome Shell.
At least you will probably find a working extension that removes the Dash ("Dock"). A search for "Hide Dash" reveals several extensions. No Dash in Overview and Hide Dash (new) are two options that work on the latest Ubuntu LTS 20.04.
Hiding the Search box may be more difficult. An old extension, Disable Search, has not been updated.