You can search Netflix and Disney+ content by linking your accounts to the Play Movies app. To do so, open the app menu and go to "Manage services," and you'll see a selection of streaming services which you can add.
With that done, if you search for a TV show or movie through Play Movies, you'll see options from your streaming services as well as from the Play store. If you want to watch the content, you'll need to have the relevant apps installed on your device. Currently, this feature is only available within the US, and does not support the streaming of live TV.
This brings Play Movies in line with Apple TV, which offers a similar universal search function. With the addition of Netflix and Disney+, Google Play can now search through the majority of the most popular streaming services, with the exception of Apple TV+.