Time Machine backup to Airport Extreme AirDisk
Question: Is the [AEBS + USB/AirDisk + Time Machine] combo finally,
  officially supported? On Mountain Lion or something? I couldn't find
  documentation along those lines but since we're talking about backups,
  I just want to make sure I'm not following an unsupported mechanism.


It was not supported as of Mountain Lion (see OS X Mountain Lion: Disks you can use with Time Machine) but according to the newest KB article (Use Time Machine to back up or restore your Mac) it is now officially supported:


  Time Machine is the built-in backup feature of your Mac. To use it, you
  need an external storage solution, sold separately:
  
  
  External hard drive connected to a USB, FireWire, or Thunderbolt port on your Mac 
  Time Capsule or macOS Server on your network 
  External hard drive connected to the USB port of an AirPort Extreme base station on your network  
  


I couldn't find any information about whether this functionality was added as an Airport Express firmware update or was introduced with a specific OS version (or both), and thus I can't provide a firmware/OS version support matrix, but from 
Backup disks you can use with Time Machine the minimum requirements seem to be:


AirPort Extreme 802.11ac model
Yosemite (OS X 10.10) (the earliest OS that references the article above, see OS X Yosemite: Back up your files with Time Machine)