feat(FN-4068): add branch conflict detection and recovery for stale worktre

Implements branch conflict detection and recovery across the Fusion engine, CLI, and dashboard — surfacing git worktree conflicts when tasks conflict with unrelated branch state, and providing a recovery workflow to resolve them. The executor and worktree pool now integrate typed branch conflict che

Fusion-Task-Id: FN-4068

packages/engine/src/index.ts

@@ -90,6 +90,18 @@ export {
 } from "./agent-instructions.js";
 export { HEARTBEAT_PROCEDURE, HEARTBEAT_SYSTEM_PROMPT, HEARTBEAT_NO_TASK_SYSTEM_PROMPT } from "./agent-heartbeat.js";
 export { WorktreePool, scanIdleWorktrees, cleanupOrphanedWorktrees, reapOrphanWorktrees } from "./worktree-pool.js";
+export {
+  BranchConflictError,
+  isBranchConflictError,
+  inspectBranchConflict,
+  listBranchRecoveryCandidates,
+  type BranchConflictCommit,
+  type BranchConflictDetails,
+  type BranchRecoveryCandidate,
+  type BranchConflictInspectionResult,
+  type InspectBranchConflictInput,
+  type ListBranchRecoveryCandidatesInput,
+} from "./branch-conflicts.js";
 export { generateReservedWorktreeName, generateWorktreeName, planTaskWorktreePath, slugify } from "./worktree-names.js";
 export { createLogger, type Logger } from "./logger.js";
 export { fetchWebContent, assertSafeUrl, WebFetchError, type WebFetchOptions, type WebFetchResult, type WebFetchErrorCode } from "./web-fetch.js";