Stats line moves into the InputBar's new footer slot (sharing the card's
width column) and expands to the design's grouped detail row: turns/steps,
LLM and tool wall time, cache hit, and input/output token split, all
derived client-side from the snapshot. The composer stack owns one 8px
rhythm, the seat fades the transcript through a fixed 36px gradient band,
back-to-bottom follows a live --dsh-composer-height, and goal/todo strips
share one 752px tip-fill column.