I got a call from a friend recently asking me "Jo, why don't I have a search bar on my Facebok Page?"
I asked them to make me an Admin - or Manager as it is called in the Admin Roles section - so that I could get a proper look at the nature of the beast.
Setting Up A Facebook Business Account and Page
And that's when we realised. They had set up the page using an email address not a personal profile - so it was actually a Facebook Business Account. These have always had far less functionality than proper personal profiles or business pages that have been set up using personal profiles. And, clearly, the option to search Facebook is one of the privileges that is denied to them.
To ensure that they set up three or four personal profiles - real people - to be Admins/Managers and then not to use that business page log in in future. Once logged in as a personal profile, the search bar functionality returned.
In these days, there is really very little reason to >set up a Facebook Page as a Business Account. If you're doing it on behalf of a client or group of people, then someone should create the page from their own personal profile and make the others admins. If the client no longer wants you to be part of that account, they can remove you or you can remove yourself.
In any event, when creating a Facebook Page, it is always a good idea to have several people as Admins/Managers so there is no chance of losing the page because the sole personal profile behind it gets shut down as a result of something that Facebook considers a transgression. They can do this without warning. If your personal profile is closed, you no longer have access to any business pages of which you may have been Admin/Manager. If there are other people listed on that page, you do not lose control of the Page altogether.