fix(delegate-task): harden child-session fallback bootstrap and cleanup

Capture delegated child-session retry context before the first prompt so fallback recovery still works when session history is empty. Align background and sync launch paths around the same bootstrap contract, clear session-scoped fallback state on every terminal path, and lock the behavior with regression coverage for first-prompt retries, exhaustion, isolation, and cleanup.

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/shared/delegated-child-session-bootstrap.ts

@@ -0,0 +1,55 @@
+import type { FallbackEntry } from "./model-requirements"
+import type { ModelFallbackControllerAccessor } from "../hooks/model-fallback"
+import { createInternalAgentTextPart } from "./internal-initiator-marker"
+import { SessionCategoryRegistry } from "./session-category-registry"
+
+export type DelegatedChildSessionRetryPart = {
+  type: "text"
+  text: string
+}
+
+export type DelegatedChildSessionBootstrap = {
+  retryParts: DelegatedChildSessionRetryPart[]
+}
+
+const delegatedChildSessionBootstrapMap = new Map<string, DelegatedChildSessionBootstrap>()
+
+export function createDelegatedChildSessionRetryParts(promptText: string): DelegatedChildSessionRetryPart[] {
+  return [createInternalAgentTextPart(promptText)]
+}
+
+export function registerDelegatedChildSessionBootstrap(args: {
+  sessionID: string
+  promptText: string
+  fallbackChain?: FallbackEntry[]
+  category?: string
+  modelFallbackControllerAccessor?: ModelFallbackControllerAccessor
+}): void {
+  delegatedChildSessionBootstrapMap.set(args.sessionID, {
+    retryParts: createDelegatedChildSessionRetryParts(args.promptText),
+  })
+
+  args.modelFallbackControllerAccessor?.setSessionFallbackChain(args.sessionID, args.fallbackChain)
+  if (args.category) {
+    SessionCategoryRegistry.register(args.sessionID, args.category)
+  }
+}
+
+export function getDelegatedChildSessionBootstrap(sessionID: string): DelegatedChildSessionBootstrap | undefined {
+  const bootstrap = delegatedChildSessionBootstrapMap.get(sessionID)
+  if (!bootstrap) {
+    return undefined
+  }
+
+  return {
+    retryParts: bootstrap.retryParts.map((part) => ({ ...part })),
+  }
+}
+
+export function clearDelegatedChildSessionBootstrap(sessionID: string): void {
+  delegatedChildSessionBootstrapMap.delete(sessionID)
+}
+
+export function clearAllDelegatedChildSessionBootstrap(): void {
+  delegatedChildSessionBootstrapMap.clear()
+}