This Project will no longer be supported due to a new project that brings more flexibility and combustibility to the header buttons
There has been quite a bit of discussion around the search option being hidden with 2.8 and that was also what i experienced.
A common approach to this in modern software is to have a search option in the topbar, clearly visible for everybody and i thik its a nice place for a search option. However the blender search is for operators so it might not be what one might expect when comparing to other software that do this.
Nonetheless i created this small addon which adds a button to the topbar to do the search.
EDIT: the button needed to be moved to the 3D View header due to viewport dependencies.