Update managed identity docs with latest best practices

[scottaddie]

Summary

• Use a different ctor for system-assigned managed identity, to make the intent clearer. The ctor currently used will soon be deprecated (see Deprecate legacy ManagedIdentityCredential ctors Azure/azure-sdk-for-net#53800).
• Update guidance for when to call UseCredential.
• Only recommend Microsoft.Extensions.Azure for client registration.

---

Internal previews

📄 File	🔗 Preview link
docs/azure/sdk/authentication/system-assigned-managed-identity.md	docs/azure/sdk/authentication/system-assigned-managed-identity

[Copilot]

Pull Request Overview

This PR simplifies managed identity authentication code samples by removing redundant local development fallback logic and relying on the framework's default DefaultAzureCredential behavior when no explicit credential is provided.

• Removed explicit DefaultAzureCredential instantiation in development environments
• Updated documentation to clarify that DefaultAzureCredential is created automatically by the framework
• Cleaned up unused imports and duplicate code snippets

Reviewed Changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
docs/azure/sdk/snippets/authentication/user-assigned-managed-identity/Program.cs	Removed unused imports, simplified credential logic to only explicitly handle production/staging environments
docs/azure/sdk/snippets/authentication/system-assigned-managed-identity/Program.cs	Removed unused imports, simplified credential logic to only explicitly handle production/staging environments
docs/azure/sdk/includes/implement-user-assigned-identity.md	Updated documentation to reflect automatic DefaultAzureCredential creation and removed references to removed code snippets
docs/azure/sdk/includes/implement-system-assigned-identity.md	Updated documentation to reflect automatic DefaultAzureCredential creation and removed references to removed code snippets
docs/azure/sdk/authentication/system-assigned-managed-identity.md	Updated publication date