feat(web): render Code Mode sub-calls as native rows nested under the run_code row

The client indexes tool/code-dispatch events into
ConversationSnapshot.codeDispatches (parent callId -> ToolResultNode-shaped
sub-calls; live mux and history replay build the identical index). ChatView
renders each run_code parent as the new code variant (description summary,
program as the expanded monospace body) with its sub-dispatches as
always-visible indented rows — every sub-row dispatches through the SAME
keyed conversation.chat.toolview hole with the same GenericToolCard
fallback, so custom registrations (bash sample) take over sub-rows exactly
as top-level rows. The details panel resolves sub-callIds to full logged
args and complete output through the native path.

Evidence: fixture turn 64 + built-bundle jsdom snapshot, real-machinery
jsdom suites (nesting, error state, details, running parent, reference
stability), and a recorded code-mode browser e2e round (keyless replay +
aria golden). Scaffold gains a toolsMode patch knob.

packages/client/runtime/src/client/sessions/conversation.ts

@@ -127,6 +127,17 @@ export type ConversationNode =
   | ToolResultNode
   | UnknownSurfaceNode
 
+/**
+ * One `run_code` sub-dispatch materialized as a {@link ToolResultNode} so every
+ * consumer (tool rows, details panel) renders it through the exact components
+ * that render a native settled call. Never part of the surface `nodes` flow —
+ * sub-calls live under their parent via {@link ConversationSnapshot.codeDispatches}.
+ * `callId` is the deterministic sub-call id (`<parent>:code:<n>`); `call`
+ * carries the sub-tool name and its JSON-stringified logged arguments;
+ * `content`/`isError` are the sub-call's complete logged outcome.
+ */
+export type CodeSubCall = ToolResultNode
+
 /** In-flight tool card material: tool/call seen, tool/result not yet. */
 export interface RunningToolCall {
   callId: string
@@ -212,6 +223,13 @@ export interface ConversationSnapshot {
   foldDegraded: boolean
   partial: PartialAssistant | null
   runningCalls: readonly RunningToolCall[]
+  /**
+   * `run_code` sub-dispatches grouped under their parent callId, in dispatch
+   * order. Populated from in-window `tool/code-dispatch` events (live and
+   * replay identically); the per-parent array reference is stable across
+   * unrelated snapshot swaps (memo premise, same regime as `nodes`).
+   */
+  codeDispatches: ReadonlyMap<string, readonly CodeSubCall[]>
   pending: readonly PendingInteraction[]
   running: boolean
   /** Input-area shape (see {@link ComposerPhase}); derived here, switched on by consumers. */