Google has lately been stricter in allowing users to sideload apps on Android devices. Play Protect is starting to use a stronger security model and will later require biometric authentication before sideloading. Even so, Google still wants to give users flexibility in using Android devices.
They are currently testing the ability to update side-loaded applications on the device through the Play Store. It will also support apps downloaded from other app stores. Users will soon see the "Update from Play" button on the Play Store listing. In addition, a warning informing the user of the origin of the application is also displayed.
For now this feature is still not given to all users. Also not sure is, will the user continue to update the application in the Play Store after pressing Update to Play.