Mi Mover, the official Xiaomi app, is still here, no need to worry
It soon became clear that there is a famous app called Mi Mover able to do the job, however, after visiting Google Play, no joy! Some alternatives circulating here and there I could not trust.
The next day I needed to change some settings. While I opened this and that, what did I see? Mi Mover! It turns out (perhaps common knowledge to a lot of people but not to me!) that Xiaomi finally included this functionality in the Settings.
You can find Mi Mover going to System Settings, then to the System & Device Settings section, then to Additional Settings. Scroll the long list and the last option you will find is Mi Mover!
When you run Mi Mover the first thing it does is to search automatically for your second device to connect to and make all transfers. Enjoy!