Four Times the Width

It did. Quality rose at every single length, including the longest ones, so the extra capacity supplied exactly what was missing.

It did not. The lift is small at every length — between 0.3 and 0.6 points — while the fall from 5 words to 60 words is essentially unchanged: 14.4 points at $d = 256$ against 14.2 at $d = 1024$. The curve shifted up and kept its shape.

The improvement is too small to matter, which shows the information is being lost in the decoder rather than in the context vector.

The lift grows with length, so extrapolating, a vector of roughly 4096 dimensions would hold even a 60-word sentence and flatten the curve.