feat(compaction): add delegated agent sessions section with resume directive

Adds §8 to compaction prompt instructing the LLM to preserve spawned agent
session IDs and resume them post-compaction instead of starting fresh.
Injects actual TaskHistory data when BackgroundManager is available.

src/hooks/compaction-context-injector/hook.ts

@@ -1,3 +1,4 @@
+import type { BackgroundManager } from "../../features/background-agent"
 import {
   createSystemDirective,
   SystemDirectiveTypes,
@@ -47,9 +48,25 @@ When summarizing this session, you MUST include the following sections in your s
 
 This section is CRITICAL for reviewer agents (momus, oracle) to maintain continuity.
 
+## 8. Delegated Agent Sessions
+- List ALL background agent tasks spawned during this session
+- For each: agent name, category, status, description, and **session_id**
+- **RESUME, DON'T RESTART.** Each listed session retains full context. After compaction, use \`session_id\` to continue existing agent sessions instead of spawning new ones. This saves tokens, preserves learned context, and prevents duplicate work.
+
 This context is critical for maintaining continuity after compaction.
 `
 
-export function createCompactionContextInjector() {
-  return (): string => COMPACTION_CONTEXT_PROMPT
+export function createCompactionContextInjector(backgroundManager?: BackgroundManager) {
+  return (sessionID?: string): string => {
+    let prompt = COMPACTION_CONTEXT_PROMPT
+
+    if (backgroundManager && sessionID) {
+      const history = backgroundManager.taskHistory.formatForCompaction(sessionID)
+      if (history) {
+        prompt += `\n### Active/Recent Delegated Sessions\n${history}\n`
+      }
+    }
+
+    return prompt
+  }
 }

src/hooks/compaction-context-injector/index.test.ts

@@ -15,6 +15,7 @@ mock.module("../../shared/system-directive", () => ({
 }))
 
 import { createCompactionContextInjector } from "./index"
+import { TaskHistory } from "../../features/background-agent/task-history"
 
 describe("createCompactionContextInjector", () => {
   describe("Agent Verification State preservation", () => {
@@ -69,4 +70,47 @@ describe("createCompactionContextInjector", () => {
     expect(prompt).toContain("Do NOT invent")
     expect(prompt).toContain("Quote constraints verbatim")
   })
+
+  describe("Delegated Agent Sessions", () => {
+    it("includes delegated sessions section in compaction prompt", async () => {
+      //#given
+      const injector = createCompactionContextInjector()
+
+      //#when
+      const prompt = injector()
+
+      //#then
+      expect(prompt).toContain("Delegated Agent Sessions")
+      expect(prompt).toContain("RESUME, DON'T RESTART")
+      expect(prompt).toContain("session_id")
+    })
+
+    it("injects actual task history when backgroundManager and sessionID provided", async () => {
+      //#given
+      const mockManager = { taskHistory: new TaskHistory() } as any
+      mockManager.taskHistory.record("ses_parent", { id: "t1", sessionID: "ses_child", agent: "explore", description: "Find patterns", status: "completed", category: "quick" })
+      const injector = createCompactionContextInjector(mockManager)
+
+      //#when
+      const prompt = injector("ses_parent")
+
+      //#then
+      expect(prompt).toContain("Active/Recent Delegated Sessions")
+      expect(prompt).toContain("**explore**")
+      expect(prompt).toContain("[quick]")
+      expect(prompt).toContain("`ses_child`")
+    })
+
+    it("does not inject task history section when no entries exist", async () => {
+      //#given
+      const mockManager = { taskHistory: new TaskHistory() } as any
+      const injector = createCompactionContextInjector(mockManager)
+
+      //#when
+      const prompt = injector("ses_empty")
+
+      //#then
+      expect(prompt).not.toContain("Active/Recent Delegated Sessions")
+    })
+  })
 })