From what I have been told, classical minor harmony also utilizes the harmonic minor.
Maybe, maybe not. That yields a +III on the mediant which isn't a basic chord in classical harmony.
I think the Rule of the Octave is a better way - certainly a historically informed way - to understand the basic classical approach to minor harmony. The rule presents a scale in the bass and shows the standard way it should be harmonized. The direction of the bass is essential to the harmony options used. An excellent, concise overview of the rule is available from the theorist Gjerdingen. Two examples rules in minor from classical masters Fenaroli and Furno are below...
Fenaroli
Furno
During the time period of these masters roman numeral analysis didn't exist. Instead they used figured bass. If the chords used for the rule are translated to roman numerals (without inversion symbols) we get the follow list...
i ii° (III) not used, typically will be I in the relative major iv IV v (minor quality, not used in cadences) V (true dominant with raised ^7 scale degree - the leading tone) (IV)VI not used, would be IV of relative major, raised ^6 scale degree is harmonized as `iv6` vii° this doesn't really appear in the rule, but would be an incomplete dominant V7 (VII) not used, the subtonic triad, would be V in the relative major
This is how harmony was taught and understood during the classical period.
The rules seek to use only fundamental harmonies of tonic, dominant, and subdominant while eschewing secondary harmonies like the mediant, submediant, subtonic, etc.
The rule doesn't mean other chords cannot be used or cannot be found in scores. It's simply a concise way to understand harmony fundamentals in the classical style.
Also, take care to distinguish between actual chords versus non-chord tone movements. Some may say you can get a augmented +III6
in minor. But that is likely to be a root position dominant where the 5th of the chord moves up to ^3
scale degree as an escape tone. Similarly you may see things that look like 7th chords, but may be analyzed as simple triads with passing tones or other non-chord tones.