feat(web): pick a session's agent preset from the composer

A seat in the composer tool row, left of the model select, showing the preset
THIS session runs — its own recorded one, not the deployment default, because a
resumed session runs what it was created with. `SessionSummary` carries
`agentPreset` for that, alongside `cwd` and `origin`.

The switch exists only while the conversation has not started. After the first
turn the seat becomes a plain label rather than a disabled menu: a greyed
control reads as "temporarily unavailable", when in fact the choice is gone for
good. The seat never asks in that state, and the host refuses independently
with `agent-preset-locked`, so a stale client cannot slip one past it.

A rejected switch restores the previous value and surfaces the host's message
rather than leaving the seat showing something the session is not running.

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

@@ -25,6 +25,8 @@ export interface SessionListEntry {
   /** Coarse durable origin for navigation filtering; not a continuation capability. */
   origin?: 'subagent'
   cwd?: string
+  /** Agent preset the session's agent was composed from (summary passthrough). */
+  agentPreset?: string
   /** Current host-computed projection values for list consumers. */
   projectionValues?: Readonly<Partial<SessionProjectionMap>>
   /** User interaction currently blocking this session, derived from live mux frames. */

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

@@ -45,6 +45,12 @@ export interface SessionSummary {
   /** Human-facing label: durable title, project basename, then session id. */
   displayTitle: string
   cwd?: string
+  /**
+   * Agent preset this session's agent was composed from; absent when the
+   * deployment composes no presets. A composer seat shows what the session
+   * actually runs rather than the deployment's current default.
+   */
+  agentPreset?: string
   parentId?: SessionId
   /** Coarse durable origin for navigation filtering; not a continuation capability. */
   origin?: 'subagent'
@@ -629,6 +635,7 @@ export class SessionsService implements ISessions {
         ...(entry.cwd !== undefined ? { cwd: entry.cwd } : {}),
         ...(entry.parentSessionId !== undefined ? { parentId: entry.parentSessionId } : {}),
         ...(entry.origin !== undefined ? { origin: entry.origin } : {}),
+        ...(entry.agentPreset !== undefined ? { agentPreset: entry.agentPreset } : {}),
       }
     }
     if (current !== undefined && currentAddress !== undefined) {

packages/client/runtime/tests/fake-api.ts

@@ -204,6 +204,8 @@ export class FakeApiClient implements IApiClient {
 
   readonly agentPresets: IApiClient['agentPresets'] = {
     list: (payload: unknown) => this.record('agentPreset.list', payload, Promise.resolve(ok({ presets: [] }))),
+    select: (payload: { agentPreset: string }) =>
+      this.record('agentPreset.select', payload, Promise.resolve(ok({ agentPreset: payload.agentPreset }))),
   }
 
   readonly skills: IApiClient['skills'] = {