It seems that the company is recreating the Chrome browser inside the Google Search application, however, without the benefits of shared cookies and logins. If you want to check whether you have still got the old Chrome browser custom tab implementation or not, you need to open a site via the Google application. Then, tap the three-dot overflow menu. This menu is available in the top right corner of your screen, and if the menu mentions ‘Powered by Chrome,’ it means that your browsing history and logins are synced across Chrome and the Google Search application.
If you are included in Google’s latest test and you want to keep using Chrome, then you can disable the in-app browser by using the settings of the Google app. You can access Google app settings via the More bottom tab available on the Google Search results page. Many people don’t like the new in-app browser since the Chrome custom tab implementation makes more sense.