[Azure .NET Generator] Override ConfigurationSchema.json generation to use AzureClients section

[m-nash]

Overview

Parent issue: #56777

The base .NET emitter (microsoft/typespec#9922) will auto-generate ConfigurationSchema.json with the well-known client name under the Clients top-level section. The Azure emitter needs to override this to place Azure SDK clients under the AzureClients section instead.

Why this is needed

• System.ClientModel clients (base emitter) → Clients section in appsettings.json
• Azure.Core clients (Azure emitter) → AzureClients section in appsettings.json

The base emitter doesn't know about the AzureClients section — it only generates schema entries under Clients. The Azure emitter must override the schema generation to:

1. Place the well-known client name under AzureClients instead of Clients
2. Reference azureOptions (which includes Retry + Diagnostics) instead of the base options
3. Reference the Azure.Identity credential definition instead of the SCM credential

What to do

Override the base emitter's ConfigurationSchema.json generation in the Azure generator to:

• Output the schema to the package's schema/ directory (sibling of src/)
• Use AzureClients as the top-level section key
• Use $ref to #/definitions/azureOptions for the Options property
• Use $ref to #/definitions/credential (Azure.Identity's definition) for the Credential property
• Include any client-specific options that extend azureOptions via allOf

Reference

• Base emitter schema issue: microsoft/typespec#9922
• Azure emitter ClientSettings override: #56617
• Design proposal: https://gist.github.com/m-nash/54dc33e269485118b8da8d8cfa8759d0
• Prototype schemas: temp/json-schema-segment-test