Term-based or embedding retrieval for a support search full of error codes and paraphrased questions?

Both. Term search is faster, cheaper and strong out of the box, and exact codes like EADDRNOTAVAIL are where it's most reliable; embeddings can blur them. Embeddings handle paraphrase and can be improved by fine-tuning, but cost more to compute, store and search.

Also check term tokenization: splitting can create false matches (“two-year-old” matching “two-factor”) or destroy identifiers. Then measure both on real queries.