It appears that Google is testing a few new features within the Search app on Android devices, as some users have noted that the hamburger menu within the app has populated a recent tab, as well as an option for lite search and the ability to enable offline search. Google is no stranger to testing new features with a small amount of users, and they often end up running tests with features throughout their various applications. Since these seem to just be tests though, there's no way of knowing when or if Google will end up implementing these changes to the Google app for all users.
For offline searches, this actually wouldn't be the first time that they have popped up as some users have been able to access them for around a few months, but it seems that Google has started to open up the functionality to a few more people. Offline searches won't be turned on automatically, but they can be enabled from the settings menu, and as part of the offline search feature there is a "manage pending searches" option that lets users see any searches that they have performed but haven't yet been completed by the app.
While offline searches is something that's already been in testing, the recent tab is completely new, and as the name of the new tab suggests when you tap on it a new page opens up where you can see a handful of your most recent searches. These appear in a side scrolling list view, and they're presented as large cards that make them easy to see and distinguish. Above the cards is a label of what the search query was and below the cards you can see when the search was completed as well as an indicator telling you the number of pages that are included with that particular search. As for Lite Mode, which also appears in the hamburger menu, the feature allows for pages to load while using less data as they will only load up the most important content by simplifying what's shown to the user. Google has added three different options for Lite Mode, and it can either be disabled, turned on all the time, or set to automatic where it will only simplify content before loading if you have a slower data connection that is detected. Overall, it seems like Google is looking to give users a way to make the Google app more useful when there is little to no internet available.