Even though Cortana can't match most of Google Assistant's functionality, it's still very handy if you have a Windows 10 PC. The app can mirror notifications to your PC, sync reminders, and provide contextual information based on your email and calendar. About a year ago, the Cortana app added an optional launcher to the lock screen, and now there's another way to open the assistant.
The latest update adds a new option, called "Cortana on Home Screen." It adds a floating Cortana button to your device, similar to a Facebook Messsenger chat head. Tapping on it opens the app instantly. Despite the name, it actually appears on the home screen and all your apps, unless you give Cortana permission to see which app is currently open (so it can tell if you're on the home screen or not).
The button is also customizable - you can choose between the Cortana logo, a circle showing your next calendar appointment, or a small rectangle. The update has already rolled out on the Play Store, but you also download it from APKMirror.