Why "Search apps", "Search files", etc. in software UIs, instead of "Search for ~"?
Solution 1:
Search here means "search in", not "search for". A more long-winded version would be "search within the apps for the thing you want" or "search within the files for the things you want".
Now, when you search within the apps, you are actually searching for an app, but that doesn't mean that "search apps" is a shortened version of "search for apps".