[System.ClientModel] Support all properties needed to create a client in ClientCache and consolidate ClientConnection.Credential usage

[ShivangiReja]

Task 1:
Enhanced the ClientCache to support client reuse based on all necessary properties required to create a client instance.

• Updated the internal cache key to account for differences in client properties including client options by adding an IEquatable<object> identifier.
• This ensures that multiple clients of the same type and same ID but with different option instances (e.g., AzureOpenAIClientOptions) are cached and retrieved independently.

Example:

project.GetAzureOpenAIChatClient("a", options1);
project.GetAzureOpenAIChatClient("a", options2);

Both clients are now stored as distinct entries if options1 != options2.

• Included a targeted test case validating the correct behavior for distinct option instances.

Task 2:
Simplified ClientConnection by removing the ApiKeyCredential property.

• All authentication details are now routed through the unified Credential property.

[azure-sdk]

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[KrzysztofCwalina]

It would be good if ClientConnection.Credential was typed as AuthenticationTokenProvider and not Object.
But I am not sure if we have time to coordinate. Maybe we just rename ClientConnection.Credential to ClientConnection.TokenProvider?

@christothes

[KrzysztofCwalina]

@ShivangiReja , @christothes, should we remove ClientConnection.ApiKeyCredential and use the ClientConnection.Credential property for API key case?

[azure-sdk]

API change check

APIView has identified API level changes in this PR and created following API reviews.

Azure.AI.OpenAI
System.ClientModel
Azure.Search.Documents
Azure.AI.Inference
Azure.AI.Projects