A few days back, folks at Android Police tore down the APK of Google App beta 7.1 and said that the company is working on adding a search widget in the notification panel and today, a reddit user has posted a video on how it may look when Google really implement it.
As you can in the see in the YouTube video, he has imagined two scenarios- one is the normal Android style Google search bar and the other one is the Fuchsia OS-based search bar, and it looks far better than what we had imagined when the news broke out.
The primary intention of having a search bar in the notification panel is to quickly search the user queries. Some might think it as a redundant feature as the home screen already has the search bar, but in the Pixel phones, Google has moved it to just a small 'G' letter in the left corner.
As of now, there's no info on when this feature will officially roll out, but it will be added in the next Android OS upgrade to the Pixel phones.