Welcome to the forums. Saving pictures from the Google app can be tricky sometimes. You can save them inside the the app from the search screen, but if you want to see the picture from the gallery sometimes you need a few more steps. Select the picture, open (visit) the page where it's included and then long press to download it.
But I got the notification something downloaded some where on my phone when I selected download image. Where is that? There's a few things in that secret location now. Images attached to see what I'm seeing and why I'm confused.