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/host/apiproxy/src/api-proxy.ts

@@ -260,11 +260,13 @@ function sessionListFields(header: SessionHeader): {
   parentSessionId?: SessionId
   origin?: 'subagent'
   cwd?: string
+  agentPreset?: string
 } {
   return {
     ...header.parentSession === undefined ? {} : { parentSessionId: header.parentSession },
     ...header.origin === undefined ? {} : { origin: header.origin },
     ...header.cwd === undefined ? {} : { cwd: header.cwd },
+    ...header.agentPreset === undefined ? {} : { agentPreset: header.agentPreset },
   }
 }
 

packages/host/apiproxy/src/api/sessions.schema.ts

@@ -55,6 +55,7 @@ export const sessionSummarySchema = z.object({
   parentSessionId: sessionIdSchema.optional(),
   origin: z.literal('subagent').optional(),
   cwd: z.string().optional(),
+  agentPreset: z.string().optional(),
   projections: z.lazy(() => sessionProjectionsBlockSchema).optional(),
 }) as unknown as z.ZodType<Wire<SessionSummary>>
 

packages/host/apiproxy/src/api/sessions.ts

@@ -156,6 +156,13 @@ export interface SessionSummary {
   origin?: 'subagent'
   /** Session working directory (header.cwd passthrough); absent when unrecorded. */
   cwd?: string
+  /**
+   * Agent preset this session's agent was composed from (header passthrough);
+   * absent when the deployment composes no presets. A surface offering a
+   * switch reads this to show what the session actually runs rather than what
+   * the deployment currently defaults to.
+   */
+  agentPreset?: string
   /**
    * Projection baseline for this row, with zero log loads: attached sessions
    * read the registry's live watermark cut; cold sessions read the persisted