As discussed in Origin of Roman Numeral Analysis, Roman numerals weren't a widespread analytical tool until at least the 19th century.
With this in mind, imagine that you're a musician in 1770; you're accustomed to the figured bass tradition, so you see excerpts like the following relatively often:
Do you conceptualize this middle harmony in a way that somehow suggests a move (however brief) towards G?
Today, we would understand this as an applied (or secondary) chord to the dominant:
But since there was no Roman-numeral analytic tradition yet, this would be an anachronistic reading for our hypothetical 1770 musician.
Would they have understood this middle chord as in some way being related to G (and perhaps moving away from C), or would they have simply understood this as "first-inversion chord with a raised sixth"? In other words, was there some other functional understanding they had for this chord?