Vector index rebuild without downtime

Design how a vector search service rebuilds its index without downtime. You host 2B 1024-dim vectors across a sharded HNSW index serving 8k QPS at 25ms p99. Periodically you must rebuild, because the embedding model was upgraded, because deletes have fragmented the graph and recall has degraded, or because you're re-sharding. The rebuild takes hours and is resource-heavy. Walk through how you rebuild a shard while it keeps serving, how you cut over without a recall cliff or a latency spike, and how you handle writes that arrive during the multi-hour rebuild.