I don’t have much experience yet transcribing vocal music and wanted to verify the appropriate way of transcribing something like this. This is an extremely long syllabic slur that carries over multiple print pages. I know that bracket slurs are used to indicate phrasing but does that mean I even have to use brackets for a slur shown between only 2 notes, such as after the appoggiaturas? Also, this is a very long run-over in the music line. Is that the best way to show it, as 1 long run-over line?
Great question - I would not use the bracket slur for the appogiatura slurs. They aren't really showing phrasing so it wouldn't be quite appropriate. I think the best option would be to use the facsimile slur, dots 56, 14, to show these. (I'd add this symbol to your SS list and perhaps even add a TN about their usage, since it is a little unusual.)
As far as the division of the phrases, that's a matter of transcriber-choice, using your artistic and musical judgement. Remember that the singer will likely memorize the music and we want to lay out the parallels in as clear a way as possible. Dividing the melisma at logical and musical points is always a good idea rather than trying to fit the entire thing into a single parallel that may end up containing 2 or 3 run-over lines. (One run-over line is fine - but any longer than that makes it hard to memorize.)
My suggestion is to sing or play through it and find good breaking points - places where a breath will be taken, for instance, or where there's a cadential feel to the phrase. The Music Code section 35.3 discusses how to show continued vowel sounds on new parallels, so be sure to reread that section as you work through the transcription.