feat(refinery): implement merge failure handling with labels and notifications

Add comprehensive failure handling for merge queue:
- Add FailureType enum with conflict, tests_fail, build_fail, flaky_test, push_fail
- Add handleFailure function that updates beads issue with labels and assignee
- Add notifyWorkerFailure for type-specific failure notifications
- Add retry logic for flaky tests (configurable via retry_flaky_tests)
- Add pushWithRetry with exponential backoff for transient push failures
- Add label support to beads UpdateOptions (AddLabels, RemoveLabels, SetLabels)

Failure actions by type:
- conflict: needs-rebase label, assign to worker
- tests_fail/build_fail: needs-fix label, assign to worker
- flaky_test: retry once, then treat as tests_fail
- push_fail: retry with backoff, needs-retry label

Closes gt-3x1.4

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/refinery/types.go

@@ -239,6 +239,59 @@ func (mr *MergeRequest) IsClosed() bool {
 	return mr.Status == MRClosed
 }
 
+// FailureType categorizes merge failures for appropriate handling.
+type FailureType string
+
+const (
+	// FailureNone indicates no failure (success).
+	FailureNone FailureType = ""
+
+	// FailureConflict indicates merge conflicts with target branch.
+	FailureConflict FailureType = "conflict"
+
+	// FailureTestsFail indicates tests failed after merge.
+	FailureTestsFail FailureType = "tests_fail"
+
+	// FailureBuildFail indicates build failed after merge.
+	FailureBuildFail FailureType = "build_fail"
+
+	// FailureFlakyTest indicates a potentially flaky test failure (may retry).
+	FailureFlakyTest FailureType = "flaky_test"
+
+	// FailurePushFail indicates push to remote failed.
+	FailurePushFail FailureType = "push_fail"
+
+	// FailureFetch indicates fetch of source branch failed.
+	FailureFetch FailureType = "fetch_fail"
+
+	// FailureCheckout indicates checkout of target branch failed.
+	FailureCheckout FailureType = "checkout_fail"
+)
+
+// FailureLabel returns the beads label for this failure type.
+func (f FailureType) FailureLabel() string {
+	switch f {
+	case FailureConflict:
+		return "needs-rebase"
+	case FailureTestsFail, FailureBuildFail, FailureFlakyTest:
+		return "needs-fix"
+	case FailurePushFail:
+		return "needs-retry"
+	default:
+		return ""
+	}
+}
+
+// ShouldAssignToWorker returns true if this failure should be assigned back to the worker.
+func (f FailureType) ShouldAssignToWorker() bool {
+	switch f {
+	case FailureConflict, FailureTestsFail, FailureBuildFail, FailureFlakyTest:
+		return true
+	default:
+		return false
+	}
+}
+
 // IsOpen returns true if the MR is in an open state (waiting for processing).
 func (mr *MergeRequest) IsOpen() bool {
 	return mr.Status == MROpen