Does any exchange provides any public information about its private keys managed BTC addresses, or is there any service that provides this information?
A few exchanges publicize their hot and cold wallets, but currently, as far as I'm aware, no exchange publishes a full list.
This may change as FATF's Recommendation 16 adoption grows, but may still be limited to closed access networks among exchanges.
Beyond that, for most services, it is not very hard to determine if a used address belongs to an exchange - most exchanges tend to follow fairly easy to identify sweeping patterns to move funds between receiver, hot, and cold wallets. Many block explorers tag various addresses to exchanges, in addition to paid coin monitoring services.