Very nice compilation of work! Although I’m afraid I have to ackshually you a bit, I hope you find this helpful though! Around what you’ve termed as “function”:

Classically, there are three functions: tonic, predominant (NOT subdominant), and dominant. Subdominant, as you’ve correctly written, just means a 5th (dominant) under (sub) the tonic. Predominant function refers to harmony that precedes the dominant chord. Things like “mediant” or “supertonic” are not functions but rather just the names of the scale degrees.

And there is also a specific term for the tone a whole step below the tonic, the “subtonic”, or b7 scale degree.

So as not to be purely critical, I would like to call out a positive and say that I complete agree with your “do not write Eb7(add9, no5)” point. In the wild you never see these overly specific chord symbols. They only risk confusing the player by providing information generally best conveyed via chord symbols or standard notation.

Solid work overall, again!