I don't think there is a specific authority for determining that a word or saying is 'officially' archaic. As for everyday language usage is the main determinant and the more reliable dictionaries can offer the best indications.
Archaic:
- (of a linguistic form) commonly used in an earlier time but rare in present-day usage except to suggest the older time, as in religious rituals or historical novels. Examples:
thou; wast; methinks; forsooth.
Archaic words:
- These words are no longer in everyday use or have lost a particular meaning in current usage but are sometimes used to impart an old-fashioned flavour to historical novels, for example, or in standard conversation or writing just for a humorous effect. Some, such as hotchpotch, reveal the origin of their current meaning, while others reveal the origin of a different modern word, as with gentle, the sense of which is preserved in gentleman. Some, such as learn and let, now mean the opposite of their former use.
List of words.
(from ODO)
Archaic words or phrases:
- Words and phrases that were used regularly in a language, but are now less common are archaic. Such words and phrases are often used deliberately to refer to earlier times. For instance, the pronoun 'thou', which is very rarely used nowadays is an archaism, which is sometimes used to suggest biblical language or a dialect.
(using.english.com)
Archaic Diction: Definition & Examples
- Have you ever read the works of Shakespeare or maybe an older version of the Bible? Doubtlessly you encountered a lot of words like 'shalt,' 'maketh,' 'thou,' or 'thine.' If words like these sound old and dusty, that's because they are. Such terms are examples of archaic diction, or archaisms, which describes words, phrases, or pronunciations that are obsolete or outdated in current usage.
(study.com/academy)