Optimizing industrial search ranking models solely for user engagement signals often introduces systematic biases, prioritizing popular or price-anchored items that may not satisfy semantic intent. We present a production-scale multi-task ranking system that integrates semantic relevance as a primary optimization objective, enabling explicit and controllable relevance--engagement trade-offs. Our architecture employs an ordinal relevance head that predicts cumulative probabilities over relevance thresholds, preserving the inherent ordering of labels. These outputs are integrated with engagement heads through a unified value model scoring function, enabling systematic balancing of semantic quality and short-term behavioral signals. To provide high-quality supervision for this multi-task framework, we utilize fine-tuned lightweight Large Language Models (LLMs) to generate three-level ordinal relevance labels: irrelevant, moderately relevant, and highly relevant. We address challenges regarding label distribution sensitivity and ensure high alignment with human annotations to enable efficient labeling for over 100 million query--item pairs. Evaluation across offline metrics, including NDCG@10, and online A/B experiments demonstrates that our approach significantly improves semantic alignment while preserving core engagement objectives.