According to reporting by 9to5Google, the Activity tab is now widely available to all users of the Google app. I was able to find it on my Android smartphone running v16.19 of the app, though it's ...

The tab is a comprehensive activity center where users can review their recent searches, access saved items, and organize collections.

The Google app is getting a new "Activity" tab that allows users to easily access their search history and saved items.

Recent activity might already be populated with call information, but you have to enable the SMS permission to “view messages from your contacts.” A prompt guides you through that process.