Change ChatClientBuilder to register singletons and support lambda-less chaining

[SteveSandersonMS]

Fixes #5572 as well as changing the default DI lifetime from scoped to singleton.

This is also needed for the API design we want in dotnet/aspire#6225

Usage with DI (common)

Before:

serviceCollection.AddChatClient(pipeline => pipeline
    .UseDistributedCache()
    .UseFunctionCalling()
    .Use(innerClientOrFactory));

After:

serviceCollection.AddChatClient(innerClientOrFactory)
    .UseDistributedCache()
    .UseFunctionCalling();

Usage without DI (uncommon)

Before:

var client = new ChatClientBuilder(serviceProvider)
    .UseDistributedCache()
    .UseFunctionCalling()
    .Use(innerClientOrFactory);

After:

var client = new ChatClientBuilder(innerClientOrFactory)
    .UseDistributedCache()
    .UseFunctionCalling()
    .Build(serviceProvider);    // Or just .Build() to use an empty service provider for scenarios where you're really not using DI at all

Summary

In the non-DI case it doesn't make much difference. It's a small improvement though, since it avoids the Use method having totally different semantics based on which oveload is called.

But in the DI case which is more common, it's simpler and more approachable as there's no need for the lambda.

It also has value for the Aspire helpers as it make it possible to do this API, which we can't otherwise achieve since you can't specify the inner client up front and can only do so once the rest of the pipeline is built.

Microsoft Reviewers: Open in CodeFlow

[SteveSandersonMS]

Note that I'll do the equivalent thing for EmbeddingGeneratorBuilder before this is merged.

[eiriktsarpalis]

Thanks, the new approach looks much more intuitive.