The Akeeba Extension Installer says 3.0.0 (Admin Tools) and 3.11.0 (Backup) are available. I changed my Download ID, then updated via the Akeeba Extension Manager installer from 2.x for each. However the updates won't go beyond 2.6.2 for Admin Tools or version 3.10.2 for Akeeba Backup.
I purge the installer cache and retry. Install proceeds "successfully" yet no update registers in the installer dialog or in either app window.
Disregard the following if you don't like rants:
(Nicholas, I love your work and your extensions, and this is not directed at you, so please pass this on, but, to me, Joomla! is like owning a vintage Jaguar - constant trouble. I've suffered through endless gotchas since v1.0 and find Wordpress so appealing and trouble-free by a long shot. Yet, I keep slugging on with Joomla! because of the enormous amount of hours I've invested, hoping against hope that before I pass on Joomla! can be appreciated by actual content creators like me and not just the programmer/troubleshooter types. Thank you. (grin) )