Extract Azure.Mcp.Core types from Microsoft.Mcp.Core

[alzimmermsft]

To prepare for the multi-server microsoft/mcp migration, we need to extract all of the Azure agnostic classes from AzureMcp.Core into a new Microsoft.Mcp.Core library.

block-beta
  columns 4
  ae["Azure.Mcp.Server"]:2
  fe["Fabric.Mcp.Server"]:2
  ak["Azure.Mcp.KeyVault"]
  as["Azure.Mcp.Storage"]
  fk["Fabric.Mcp.Lakehouse"]
  fs["Fabric.Mcp.Dashboard"]
  ac["Azure.Mcp.Core"]:2
  fc["Fabric.Mcp.Core"]:2
  mc["Microsoft.Mcp.Core"]:4

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This should include any shared classes that Fabric would need to make Fabric area libraries and a Fabric mcp server.

AzureMcp.Core should have its classes split into AzureMcp.Core and Microsoft.Mcp.Core.

These classes are Azure specific and should remain in AzureMcp.Core:

SubscriptionCommand
AzureMcpServerConfiguration
OpenTelemetryExtensions
ResourceGroupInfo
AuthMethod
AzureCredentials
ETag
AuthMethodOptions
GlobalOptions
ParseResultExtensions
RetryPolicyOptions
SubscriptionOptions
TelemetryActivityExtensions

AzureMcp.Core.Services.Azure.*
AzureMcp.Core.Services.Caching.*
AzureMcp.Core.Areas.Subscription.*

[alzimmermsft]

Copied from Azure/azure-mcp#954