Originally requested and discussed here: https://meta.wikimedia.org/wiki/Tech#Sorting. Filing this task to keep track of the code and config patches.
(Abkhaz language is also known as Abkhazian, but MediaWiki uses 'Abkhaz' in languages/data/Names.php, so I'm sticking to that.)
ICU does not support Abkhazian, but we can add support for it fairly easily, using the system that @Bawolff previously implemented for Bashkir (see T162823).