Support log telemetry for user's AppInsight instance

[srnagar]

What does this PR do?

This pull request refactors how OpenTelemetry is configured for Azure Monitor exporters, separating the logic for Microsoft-owned and user-provided Application Insights instances. It introduces clearer method naming and a new constants class to distinguish between telemetry destinations, and moves logger configuration to be handled exclusively in Azure Monitor setup.

Telemetry configuration refactoring:

• Split the generic ConfigureAzureMonitorExporter method into two specialized methods: ConfigureMicrosoftAzureMonitorExporter and ConfigureUserProvidedAzureMonitorExporter, making the configuration for Microsoft and user-provided telemetry more explicit (OpenTelemetryExtensions.cs).
• Updated the logic in EnableAzureMonitor to call the new specialized configuration methods based on the telemetry destination (OpenTelemetryExtensions.cs) [1] [2].

Constants and naming improvements:

• Added a new AppInsightsInstanceType class to define constants for distinguishing between Microsoft and user-provided Application Insights instances (TelemetryConstants.cs).
• Updated exporter configuration to use the new AppInsightsInstanceType constants for naming exporters instead of passing string literals (OpenTelemetryExtensions.cs) [1] [2].

Logger configuration changes:

• Removed OpenTelemetry logger setup from ConfigureOpenTelemetryLogger and moved logger configuration to be handled within Azure Monitor setup, preventing duplicate configuration (OpenTelemetryExtensions.cs).

GitHub issue number?

https://github.com/microsoft/mcp-pr/issues/185

Pre-merge Checklist

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[Copilot]

Pull request overview

This PR refactors OpenTelemetry configuration to separate the setup logic for Microsoft-owned and user-provided Application Insights instances. The changes introduce clearer method naming through specialized configuration methods and add a new constants class to distinguish between telemetry destinations.

Changes:

• Splits generic Azure Monitor exporter configuration into two specialized methods: one for Microsoft telemetry and one for user-provided telemetry
• Introduces AppInsightsInstanceType constants class to standardize naming for telemetry destinations
• Removes OpenTelemetry logger setup from ConfigureOpenTelemetryLogger, with logging now only configured for user-provided Application Insights

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 3 comments.

File	Description
core/Microsoft.Mcp.Core/src/Commands/TelemetryConstants.cs	Adds new AppInsightsInstanceType class with constants for Microsoft and UserProvided telemetry destinations
core/Azure.Mcp.Core/src/Extensions/OpenTelemetryExtensions.cs	Refactors Azure Monitor configuration into two specialized methods, removes logger setup from ConfigureOpenTelemetryLogger, and updates exporter naming to use new constants