fix(tools,client): chain-mode resolution and a live preset label

modeFor read only the exact scope's layer, so a `code`-preset session
advertised the native catalog: the mode is declared on the preset's STANDING
scope, and the agent only parents to it. Nearest scope wins along the chain —
the mode decides what the model SEES, which is the class of fact the chain
inherits. Caught live (the model politely computed with bash and said
run_code was not in its list); the chain test pins it.

The client half of the label fix: the create echo and the session-added
frame's agentPreset now reach the session list (newest wins in the upsert —
every producer of the field reports the CURRENT composition), and a confirmed
blank-session switch publishes through the new ISessions.noteAgentPreset, so
the header label moves with the composition instead of waiting for a reload.

packages/client/ui-agent-preset/src/client/index.ts

@@ -98,6 +98,8 @@ export function apply(ctx: ClientContext): void {
           blank: summary.blank,
           ...summary.agentPreset === undefined ? {} : { agentPreset: summary.agentPreset },
         }
+    }, (sessionId, agentPreset) => {
+      scope.sessions.noteAgentPreset(sessionId as never, agentPreset)
     })
 
     const seatInjected = (): AgentPresetSeatInjected => ({

packages/client/ui-agent-preset/src/client/seat-store.ts

@@ -60,6 +60,12 @@ export class AgentPresetSeatController {
     private readonly api: Pick<IApiClient, 'agentPresets'>,
     /** The session the hero is about to hand over to, when there is one. */
     private readonly currentSession: () => SeatSessionSummary | undefined,
+    /**
+     * Publish an applied switch into the session list, so the header label
+     * moves with the composition instead of waiting for the next full list
+     * refresh. Optional: a harness that renders no list omits it.
+     */
+    private readonly onApplied?: (sessionId: string, agentPreset: string) => void,
   ) {}
 
   private set(patch: Partial<AgentPresetSeatState>): void {
@@ -129,6 +135,7 @@ export class AgentPresetSeatController {
       }
       // Consumed: the next new session opens on the deployment default again.
       this.set({ busy: false, current: response.result.value.agentPreset })
+      this.onApplied?.(session.id, response.result.value.agentPreset)
     } catch (error) {
       this.staged = undefined
       this.set({ busy: false, error: messageOf(error), current: this.fallback })