From the Support document:
To make your personal digital assistant as helpful as possible, we’re integrating Cortana into your Microsoft 365 productivity apps. As part of this evolution, on January 31st, 2020, we’re ending support for the Cortana app on Android and iOS in your market. At that point, the Cortana content you created–such as reminders and lists–will no longer function in the Cortana mobile app or Microsoft Launcher, but can still be accessed through Cortana on Windows. Also, Cortana reminders, lists, and tasks are automatically synced to the Microsoft To Do app, which you can download to your phone for free.
After January 31st, 2020, the Cortana mobile app on your phone will no longer be supported and there will be an updated version of Microsoft Launcher with Cortana removed.
None of this is too surprising, and I'm guessing the W10M deadline for support and the Cortana announcement timing aren't just coincidence. Now Microsoft can say that from February 2020 Cortana is a productivity assistant (e.g. in Office) and a Windows desktop application without any 'Mobile assistant' context, even on 'ye olde' Windows phone.
It does beg the question of whether Cortana will stop working on Windows phones - it has to happen at some point, I suspect. We had content being removed this time last year, so I'd expect a similar break in content APIs in 2020. And, when Cortana does eventually stop responding in the future on Windows phones, no one will be able to complain in forums because the OS itself will be unsupported at that point and Microsoft can just point to iOS and Android mobiles with Siri and Google Assistant instead.
Microsoft Launcher will carry on being developed, of course, and I'll keep an eye on it, but digital assistant duties will 'just' be Google Assistant, which is - admittedly - rather brilliant. As for Surface Duo, in late 2020, the same applies, though I wouldn't rule out a Cortana application or Cortana helper in the revised Office applications for the dual screen (not a) smartphone.