Hi Raghavan, Srinivasan •,
Welcome to Microsoft Q&A forum.
As I understand, you want to know about how Encryption at Rest happens in the some Azure Services:
1). Azure AI Search: Refer: https://learn.microsoft.com/en-us/azure/search/search-security-manage-encryption-keys?tabs=portal-pp%2Cmanaged-id-sys
https://learn.microsoft.com/en-us/azure/search/search-security-get-encryption-keys
2). Azure Database for PostgreSQL: https://learn.microsoft.com/en-us/azure/postgresql/flexible-server/concepts-security
3). Azure Cache for Redis: https://learn.microsoft.com/en-us/azure/azure-cache-for-redis/cache-how-to-encryption
4). Azure Cosmos DB for PostgreSQL:
https://learn.microsoft.com/en-us/azure/cosmos-db/database-encryption-at-rest
https://learn.microsoft.com/en-us/azure/cosmos-db/postgresql/concepts-security-overview
For vector search refer:
https://learn.microsoft.com/en-us/azure/postgresql/flexible-server/how-to-use-pgvector
https://learn.microsoft.com/en-us/azure/azure-cache-for-redis/cache-overview-vector-similarity
https://learn.microsoft.com/en-us/azure/search/vector-search-overview
https://learn.microsoft.com/en-us/azure/cosmos-db/mongodb/vcore/vector-search
Hope this helps. If you have more specific service-related query, please raise service wise question so that dedicated service engineer can assist you in a better way.
Thanks.