Chopin's Etude No. 16 in A minor, Op. 25 No. 4, ends with a cadence like this:
B♭/D - A
In Roman numerals, we write as:
♭II6 - I
Is this cadence viewed as Plagal (N6 - I), or Authentic (tt - I)?
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An Authentic version would use the Dominant, which would be E7. They are most convincing to end a piece when showing the leap of a fifth down or fourth up (E-A) in the bass voice.
Here you use the sn ("Neapolitaner") of the 4th scale degree in A, d minor chord with flatted sixth instead of 5th.
The two chord progression is a plagal example showing the subdominant (d), to answer your question.
You are mistaking the coda for the ending cadences.
The cadences ending the piece are straight forward:
N6 V7 i then a deceptive cadence
N6 V7 IV followed by another PAC
N6 V7 i.
After that is the coda which is a decoration of the tonic chord. Most of it alternates the tonic and subdominant. The
N6 is put in and plays the role as a subdominant. The final chord uses the Picardy third.
You are mixing up the idea of structural cadences with the decorative elaboration of a coda.