International Components for Unicode (ICU) Date Formatter for MySQL?
I think the answer is...  Use MySQL to store dates/datetimes/timestamps in the limited formats that it provides, then use app code -- possibly some library in your app language -- to get at fancier formatting.

As a general rule, a database is responsible for storing; the application is responsible for formatting.

See also https://dev.mysql.com/doc/refman/5.7/en/locale-support.html