FN-5872: clear active-session registry on PR cleanup

Ensure PR-mode merge cleanup removes stale active-session registry state before deleting worktrees.

- unregister the task worktree from the active-session registry during merged-task artifact cleanup
- export the active-session registry from the engine entrypoint for lifecycle cleanup usage
- add CLI and engine regression coverage for registry cleanup and missing-entry best-effort behavior
- add a patch changeset for the published CLI package

Files changed:
 .changeset/fn-5872-registry-cleanup.md             |  5 ++++
 .../src/commands/__tests__/task-lifecycle.test.ts  | 29 +++++++++++++++++++++-
 packages/cli/src/commands/task-lifecycle.ts        |  8 +++++-
 .../pr-mode-worktree-invariants.test.ts            | 11 +++++---
 packages/engine/src/index.ts                       |  1 +
 5 files changed, 49 insertions(+), 5 deletions(-)

Fusion-Task-Id: FN-5872

Fusion-Task-Lineage: d4db24a3-7ae0-4d07-b029-7f30b2f65d2e

packages/engine/src/__tests__/reliability-interactions/pr-mode-worktree-invariants.test.ts

@@ -283,10 +283,15 @@ describe("FN-5420 reliability interactions: PR mode worktree invariants", () =>
     expect(releaseSpy).toHaveBeenCalledWith(path, "FN-5455-THROW");
   });
 
-  it.skip("FN-5456 follow-up required: cleanup should clear active-session registry entry", async () => {
-    const path = "/tmp/fn-5456-session";
-    activeSessionRegistry.registerPath(path, { taskId: "FN-5456", kind: "executor", ownerKey: "FN-5456" });
+  it("FN-5872: cleanup clears active-session registry entry", async () => {
+    const path = "/tmp/fn-5872-session";
+    activeSessionRegistry.registerPath(path, { taskId: "FN-5872", kind: "executor", ownerKey: "FN-5872" });
     expect(activeSessionRegistry.lookupByPath(path)).not.toBeNull();
+
+    const { cleanupMergedTaskArtifacts } = await loadPrLifecycleModule();
+    await cleanupMergedTaskArtifacts("/tmp", { id: "FN-5872", worktree: path } as any);
+
+    expect(activeSessionRegistry.lookupByPath(path)).toBeNull();
   });
 
   it("FN-5420/FN-5279: mergeIntegrationWorktree setting does not gate PR-mode processing", async () => {

packages/engine/src/index.ts

@@ -172,6 +172,7 @@ export {
   type MockScript,
   type MockScriptContext,
 } from "./providers/index.js";
+export { activeSessionRegistry } from "./active-session-registry.js";
 export { WorktreePool, scanIdleWorktrees, cleanupOrphanedWorktrees, reapOrphanWorktrees } from "./worktree-pool.js";
 export {
   pruneWorktreeAdminEntries,