Azure Monitor is the correct service for centralized monitoring and diagnostics for a Cosmos DB account.

Azure Monitor collects metrics and diagnostic logs across Azure services and provides a single place to view Cosmos DB telemetry. It can store and analyze data using an underlying Azure Log Analytics workspace and surface application traces from Azure Application Insights. It also supports alerting, dashboards and diagnostic settings that are used to track performance and overall health.

Azure Log Analytics is the workspace and query engine used to store and analyze logs and metrics. It is a component used by the central monitoring service and not the top level service that provides the full centralized monitoring and alerting experience.

Azure Application Insights is focused on application performance monitoring and developer telemetry. It is useful for app diagnostics but it is not the centralized, cross resource monitoring service for Cosmos DB account health.

Azure Advisor provides best practice recommendations for performance, security and cost optimization. It offers guidance rather than the continuous telemetry collection and alerting needed to monitor Cosmos DB performance and health.

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