Treating literacy as a continuum rather than a binary capability is good, but I don't know if citing Einhardt's biography of Charlemagne is the most solid way to do that: the blandishments are so deep it registers as a tall tale. If I recall, the claim Einhardt was making was maybe greater -- that Charlemagne understood and could read Latin perfectly well. I'm uncertain what the situation for written vernacular language was at that time.
I also have to mention that it was the Carolingian renaissance that introduced orthographic reforms like spaces between words, readable fonts, and punctuation. It was also after these reforms that silent reading became normalized (I think these things are possibly related).
> I'm uncertain what the situation for written vernacular language was at that time.
As far as I understand, spelling was standardized surprisingly recently in most western languages (usually 17th-18th century). Latin dictionaries have been around, but there weren't really dictionaries as we know them today. In such a context, it's hard to pin down what literacy even means.
I also have to mention that it was the Carolingian renaissance that introduced orthographic reforms like spaces between words, readable fonts, and punctuation. It was also after these reforms that silent reading became normalized (I think these things are possibly related).