feat(FN-5349): add integration branch resolver with auto-recovery fallback

FN-5349 adds a dedicated integration branch resolution module (`packages/engine/src/integration-branch.ts`) replacing ad-hoc dynamic fallbacks, routes merger branch conflict resolution through it, wires auto-recovery handlers (branch-worktree, contamination) to use integration branch fallback, and w

Fusion-Task-Id: FN-5349

packages/cli/src/commands/__tests__/task-lifecycle.test.ts

@@ -13,6 +13,14 @@ vi.mock("node:child_process", () => ({
       cb(err as Error, "", (err as Error).message);
     }
   },
+  execFile: (file: string, args: string[] | undefined, opts: unknown, cb: (err: Error | null, stdout: string, stderr: string) => void) => {
+    try {
+      const result = execMock(`${file} ${(args ?? []).join(" ")}`.trim(), opts);
+      cb(null, typeof result === "string" ? result : "", "");
+    } catch (err) {
+      cb(err as Error, "", (err as Error).message);
+    }
+  },
 }));
 
 import { processPullRequestMergeTask, getTaskBranchName } from "../task-lifecycle.js";