The spelling of the word "hadst dinner" may be confusing to some, but it is actually a form of the past tense of the verb "have" in the second person singular. The IPA phonetic transcription for this word would be /hædst ˈdɪnər/. Essentially, this means that "hadst" is pronounced as "had-ist" and the "dinner" part is pronounced normally. This type of spelling was commonly used in Early Modern English but is now considered archaic.
The phrase "hadst dinner" is an archaic form of the phrase "had dinner" in the second person singular past tense. It is derived from Middle English and is no longer in common use in modern English.
The etymology of the word "dinner" itself can be traced back to the Old French word "disner", which meant "to dine". This word ultimately comes from the Latin word "disjejunare", which means "to break a fast" or "to eat breakfast". Over time, the meaning of "disner" shifted to refer to the midday meal, which eventually became known as "dinner" in English.
As for the auxiliary verb "hadst", it is the second person singular past tense form of the verb "have".