While some Android makers have implemented system-wide search on their devices, it is not part of the core OS. That is about to change with Android 12 as beta 4 for the Pixel phones does support it, even if it this feature hasn’t been officially released yet. It looks like work on it is still ongoing as it appears incomplete.
Right now you can only access it through the search bar in the app drawer, the search widget on the homescreen still uses the old search feature. For the app drawer, a neat new option can make the keyboard pop up every time you open the app drawer, allowing you to instantly start typing to find what you are looking for.
Here is system-wide search in action:
The on-device system-wide search can look through the following: shortcuts (for apps and people), people (contacts, but also conversations with them), settings (including toggles and other controls) and tips. You can disable each category individually if you don’t want it in the results.
Google is apparently experimenting with adding even more search categories, however that doesn’t seem ready for prime time. Neither does the feature itself to be fair. Still, this is something that iOS users have been enjoying for years and will be a great addition to Android.
There is a way to activate system-wide search, though it only works on rooted Pixels and you need a Magisk module developed by kdrag0n, which is available to the developer’s Patreon supporters.