feat(agents): Tier 2 — AGENTS.md + per-session picker

Six builtin defaults (Code Reviewer, Debugger, Refactorer, Architect,
Security Auditor, Prompt Builder) with no model field so session.model
wins. Project root AGENTS.md parsed on demand with mtime cache; when
present, only its agents are shown. sessions.agent_id resolves per turn
into effective system prompt, temperature, and a tool whitelist applied
in inference. AgentPicker mounts in the ChatInput toolbar; SettingsDrawer
agent surface deferred to Batch 7.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/web/src/api/client.ts

@@ -8,6 +8,7 @@ import type {
   SidebarResponse,
   ListDirResult,
   ViewFileResult,
+  AgentsResponse,
 } from './types';
 
 export class ApiError extends Error {
@@ -93,7 +94,7 @@ export const api = {
       request<Session[]>(`/api/projects/${projectId}/sessions${status ? `?status=${status}` : ''}`),
     create: (
       projectId: string,
-      body: { name?: string; model?: string; system_prompt?: string }
+      body: { name?: string; model?: string; system_prompt?: string; agent_id?: string | null }
     ) =>
       request<Session>(`/api/projects/${projectId}/sessions`, {
         method: 'POST',
@@ -102,7 +103,7 @@ export const api = {
     get: (id: string) => request<Session>(`/api/sessions/${id}`),
     update: (
       id: string,
-      body: Partial<Pick<Session, 'name' | 'model' | 'system_prompt'>>
+      body: Partial<Pick<Session, 'name' | 'model' | 'system_prompt' | 'agent_id'>>
     ) =>
       request<Session>(`/api/sessions/${id}`, {
         method: 'PATCH',
@@ -179,6 +180,11 @@ export const api = {
 
   models: () => request<ModelInfo[]>('/api/models'),
 
+  agents: {
+    list: (projectId: string) =>
+      request<AgentsResponse>(`/api/projects/${projectId}/agents`),
+  },
+
   settings: {
     get: () => request<Record<string, unknown>>('/api/settings'),
     patch: (body: Record<string, unknown>) =>