Welcome to the forum!
First of all, what exactly do you mean by “home screen”? That’s a term commonly used with regard to smartphones.
If you’re talking about the desktop environment, then Manjaro is available with about a dozen ─ give and take ─ different desktop environments, each of which has its own features. We don’t know what you have chosen ─ our crystal ball is currently in for repairs.
If your desktop environment is KDE Plasma, then yes, if no window is active on the virtual desktop you’re currently on, then you can start typing the names of applications and/or documents, and then you will get a drop-down menu with items to choose from. However, if there is an active application on your current desktop ─ meaning that the window has the mouse focus ─ then you need to press Alt+F2 to bring up the search.
Of course, this is for KDE Plasma. I don’t know whether this feature is supported in GNOME, XFCE, LXDE, LXQt, Budgie, Cinnamon, MATE or Deepin, let alone the standalone window managers like i3, OpenBox or whatever else there is.
In addition to that, the search is of course also limited to what’s installed on your system. If you want to search for available applications that have not (yet) been installed on your system, then you need to search for them in Pamac, or alternatively, in Octopi.