Globally-distributed search index

Design a globally-distributed search index for a SaaS where merchants in the US, EU, and APAC all need < 30ms search latency from their nearest region, but the catalog is written from one merchant's primary region and must appear in search worldwide within ~10s. 100k tenants, hugely skewed (one tenant has 50M products, most have a few thousand). How do you replicate the index across regions, keep all regions fresh, and handle the giant tenant without it starving the small ones?