feat(web): turn speed metrics and composer context meter

Assistant footers and the stats line gain TTFT/tok-per-second readings
folded from step timings; context occupancy moves off the stats line onto
a composer ring whose panel shows a heuristic system/tools/messages
breakdown from the new token-meter contextBreakdown session projection.

packages/llm/token-meter/src/projection.ts

@@ -40,11 +40,30 @@ export interface ContextPressureProjection {
   contextWindow?: number
 }
 
+/**
+ * Heuristic composition of the next request's context: what the prompt is
+ * made of, not what it costs. All three figures use the meter's fixed
+ * density estimate (they will not sum exactly to the provider-reported
+ * `pressureTokens`, which is billing-grade and one request behind), and the
+ * message figure tracks the live surface, so it moves as content is appended
+ * or compacted while the provider number holds still.
+ */
+export interface ContextBreakdownProjection {
+  /** Heuristic tokens of the newest request envelope's system prompt; 0 before any request. */
+  systemTokens: number
+  /** Heuristic tokens of the newest request envelope's tool schemas; 0 before any request. */
+  toolsTokens: number
+  /** Heuristic tokens of the current model-visible conversation surface. */
+  messageTokens: number
+}
+
 declare module '@deepseek-ai/dsh-session-projection/types' {
   interface SessionProjectionMap {
     /** Provider-reported usage accumulated across the complete durable log. */
     tokenUsage: TokenUsageProjection
     /** Newest request pressure paired with the newest known route capacity. */
     contextPressure: ContextPressureProjection
+    /** Heuristic system/tools/message composition of the next request. */
+    contextBreakdown: ContextBreakdownProjection
   }
 }