Now, 12 hours later, the situation reported persists. LanguageStats reports 1 message for MediaWiki and 1 for MediaWiki core. Going into MediaWiki, however, there are several messages waiting for translation, not 1. It seems, at this time, that MediaWiki groups other than MediaWiki core are not being counted by LanguageStats.
I noticed that it is now apparently possible to purge the cache - that has not been possible for some time. So, I just purged LanguageStats and some people should now realise there have been 17 MediaWiki messages waiting for translation for a couple of days.
Thanks for patience. I have a hunch what could cause this and will investigate. Due to holidays, except a response next week.