[Azure Mgmt Generator] Fix method ordering to put async methods first across all providers

[Copilot]

This PR fixes the method ordering in the Azure Management Generator to match the behavior of the old generator. Previously, the new generator was outputting sync methods first followed by async methods, but the old generator put async methods first.

Problem

The current generator produces code like this:

// Sync method first
public virtual Response<ZooResource> Get(CancellationToken cancellationToken = default) { ... }

// Async method second  
public virtual async Task<Response<ZooResource>> GetAsync(CancellationToken cancellationToken = default) { ... }

But the old generator produced:

// Async method first
public virtual async Task<Response<ZooResource>> GetAsync(CancellationToken cancellationToken = default) { ... }

// Sync method second
public virtual Response<ZooResource> Get(CancellationToken cancellationToken = default) { ... }

Solution

Updated method ordering to generate async methods before sync methods across all providers:

ResourceClientProvider: Fixed ordering in three locations:

• Paging methods: Changed order from (sync, async) to (async, sync)
• Update operations: Changed order from (sync, async) to (async, sync)
• Other resource operations: Changed order from (sync, async) to (async, sync)

MockableResourceProvider: Fixed ordering in two locations:

• Non-resource methods: Changed to add async method before sync method
• Get methods: Changed to yield async method before sync method

ResourceCollectionClientProvider: Already correct - uses { true, false } pattern consistently.

Verification

Generated test projects now show async methods appearing first in all resource classes, collection classes, and mockable providers. All 51 existing tests continue to pass. Generated code compiles successfully with no functional changes, only ordering changes.

This change reduces the code diff when switching from the old generator to the new generator, making the migration smoother.

Fixes #51834.

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[Copilot]

Pull Request Overview

This PR fixes method ordering in the Azure Management Generator to ensure async methods appear before sync methods across all providers, matching the behavior of the old generator. Previously, the new generator was outputting sync methods first followed by async methods, which created unnecessary diffs when migrating from the old to new generator.

• Fixed method ordering in ResourceClientProvider for paging, update, and other resource operations
• Fixed method ordering in MockableResourceProvider for non-resource and get methods
• Ensures async methods consistently appear before sync methods across all generated code

Reviewed Changes

Copilot reviewed 2 out of 10 changed files in this pull request and generated no comments.

File	Description
ResourceClientProvider.cs	Reordered method generation to put async methods before sync methods for paging operations, update operations, and other resource operations
MockableResourceProvider.cs	Reordered method generation to put async methods before sync methods for non-resource methods and get methods

[live1206]

/check-enforcer override