This is the result of some changes to the angular implementation introduced in v4.7.21, which among other things, implements asset caching to improve the performance of angular built pages (such as the mailing interface).
The folder where those asset cache files are stored must be directly accessible (in Joomla, that folder is: media/civicrm/persist/contribute/dyn/). If it's not, it will throw console errors and fail to render the page.
In your case, you were using AdminTools to generate your .htaccess file, and that included directives which blocked direct access to files in that folder. By adding that folder to the exclusion list and rebuilding your .htaccess file, you can now render the screen.
The other option is to go to Administer > System Settings > Debugging and error handling --- and turn asset caching off.
Additional details (and other recommended folder exclusions in AdminTools) can be found here: https://docs.civicrm.org/user/en/latest/website-integration/integrating-with-joomla/#configurationconflicts-with-common-extensions