Web composer stats detail row and input-zone polish

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.

packages/client/ui-conversation/README.md

@@ -34,7 +34,7 @@ None; this package neither assembles nor sends a provider request.
 
 ## Known Limitations and Deferred Work
 
-- **The stats line has no duration segment** — assistant `usage` carries token accounting only; elapsed-time needs a host data source.
+- **Stats-line durations cover the in-window flow only** — LLM and tool wall times fold the snapshot's assistant `timing` and tool call/result pairs, so nodes outside the loaded event window (older history) are not counted.
 - **Details panel is the minimal form and currently has no entry point** — selected call args/result raw display; the Input/Output/Metadata switch, Prev/Next stepping, and See-in-trajectory deep link are deferred. Tool rows stopped being details-panel click targets and nothing replaced that gesture, so `ChatViewInjected.openDetails` is implemented but uncalled and the panel (including its terminal card) is unreachable in the assembled application; its rendering stays covered by mounting it with a selection directly.
 - **Assistant per-message paging is a reserved slot** — drawn in the design, not implemented. The finalized IconActions row (copy / branch / clock) ships; branch remains a chrome stub.
 - **The sparkle icon for the others tool row is a hand-drawn approximation** — the design glyph's vector geometry is not exportable locally; promotion into ui-primitives waits on an exact export.