Word/term for a stick in the mud authority?
As RsutyUK points out, Dinosaur would be fitting here, in the sense of being someone out-of-touch with modern practices and especially technology. It's certainly commonly used in business for directors (or even key people in politics) who get in the way of progress because of their antiquated ideas.
an old-fashioned person or thing that people no longer consider to be useful
https://dictionary.cambridge.org/dictionary/english/dinosaur
fossil
- slang. Someone whose views are outdated or old-fashioned.
Please tell me you're not one of those fossils who expects women to get married as soon as they graduate college.
Source: https://idioms.thefreedictionary.com/fossil