The newest version of the Google app Beta is hinting at a notification panel search bar. While there is no clear answer for when Google will implement this feature in the app it does appear that Google is laying the foundation for introducing it at some point, and they could even be testing it internally. There are a lot of unknowns about this new change for the moment, such as how the search bar will appear visually and where Google plans to put it, but a string of code in the latest Google app Beta APK makes a reference to a "quick search bar" while also referencing the act of showing it in the notification panel. It seems pretty clear what Google wants to do here, and perhaps they'll end up bringing this feature to users sooner than later.
While having a search bar in the notification panel would be a convenience thing for many users it's probably safe to say that not all users will want to have a search bar persistently hanging out in the notification panel, so it will be interesting to see how Google ends up working this in, and whether or not they will give users the option to disable it if they don't want it there.
In addition to this potential new feature it also looks like Google is going to start informing users about the pollen count. An icon found in the APK points to Google detailing what the pollen count will be like on a given day, though with this simply being an icon and nothing else at the moment there isn't any information about where these details will reside location-wise. Regardless of location though it should be pretty useful information for those that suffer from allergies due to pollen as it will be able to help them better prepare for an excursion outside so they aren't as affected. This is another feature that is not quite yet live and there is no indication of when Google plans to incorporate the new info but it may not be too far off if they're already inserting the icon that will accompany the actual data.