Add CarbonOptimization SDK for first time (Azure#49528)

Author: liangchenmicrosoft

sdk/carbon/Azure.ResourceManager.CarbonOptimization/Azure.ResourceManager.CarbonOptimization.sln

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+Microsoft Visual Studio Solution File, Format Version 12.00
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sdk/carbon/Azure.ResourceManager.CarbonOptimization/CHANGELOG.md

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+# Release History
+
+## 1.0.0-beta.1 (2025-05-15)
+
+### Features Added
+
+This package follows the [new Azure SDK guidelines](https://azure.github.io/azure-sdk/general_introduction.html), and provides many core capabilities:
+
+    - Support MSAL.NET, Azure.Identity is out of box for supporting MSAL.NET.
+    - Support [OpenTelemetry](https://opentelemetry.io/) for distributed tracing.
+    - HTTP pipeline with custom policies.
+    - Better error-handling.
+    - Support uniform telemetry across all languages.
+
+This package is a Public Preview version, so expect incompatible changes in subsequent releases as we improve the product. To provide feedback, submit an issue in our [Azure SDK for .NET GitHub repo](https://github.com/Azure/azure-sdk-for-net/issues).
+
+> NOTE: For more information about unified authentication, please refer to [Microsoft Azure Identity documentation for .NET](https://docs.microsoft.com//dotnet/api/overview/azure/identity-readme?view=azure-dotnet).

sdk/carbon/Azure.ResourceManager.CarbonOptimization/Directory.Build.props

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+<Project ToolsVersion="15.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <!--
+    Add any shared properties you want for the projects under this package directory that need to be set before the auto imported Directory.Build.props
+  -->
+  <Import Project="$([MSBuild]::GetDirectoryNameOfFileAbove($(MSBuildThisFileDirectory).., Directory.Build.props))\Directory.Build.props" />
+</Project>

sdk/carbon/Azure.ResourceManager.CarbonOptimization/README.md

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+# Microsoft Azure CarbonOptimization management client library for .NET
+
+Azure carbon optimization helps organizations measure and minimize the carbon impact of their Azure footprint. With this service, you can:
+
+    - Track and analyze emissions across Azure resources and subscriptions.
+    - Access carbon emissions data and insights via REST APIs and CSV exports.
+    - Optimize resource utilization to lower emissions and costs.
+
+As part of Microsoft's commitment to sustainability and environmental responsibility, and by using it, you can align your cloud strategy with your sustainability goals and demonstrate your leadership in addressing the global climate challenge.
+
+This library follows the [new Azure SDK guidelines](https://azure.github.io/azure-sdk/general_introduction.html), and provides many core capabilities:
+
+    - Support MSAL.NET, Azure.Identity is out of box for supporting MSAL.NET.
+    - Support [OpenTelemetry](https://opentelemetry.io/) for distributed tracing.
+    - HTTP pipeline with custom policies.
+    - Better error-handling.
+    - Support uniform telemetry across all languages.
+
+## Getting started
+
+### Install the package
+
+Install the Microsoft Azure CarbonOptimization management library for .NET with [NuGet](https://www.nuget.org/):
+
+```dotnetcli
+dotnet add package Azure.ResourceManager.CarbonOptimization --prerelease
+```
+
+### Prerequisites
+
+* You must have an [Microsoft Azure subscription](https://azure.microsoft.com/free/dotnet/).
+
+### Authenticate the Client
+
+To create an authenticated client and start interacting with Microsoft Azure resources, see the [quickstart guide here](https://github.com/Azure/azure-sdk-for-net/blob/main/doc/dev/mgmt_quickstart.md).
+
+## Key concepts
+
+Key concepts of the Microsoft Azure SDK for .NET can be found [here](https://azure.github.io/azure-sdk/dotnet_introduction.html)
+
+## Documentation
+
+Documentation is available to help you learn how to use this package:
+
+- [Quickstart](https://github.com/Azure/azure-sdk-for-net/blob/main/doc/dev/mgmt_quickstart.md).
+- [API References](https://docs.microsoft.com/dotnet/api/?view=azure-dotnet).
+- [Authentication](https://github.com/Azure/azure-sdk-for-net/blob/main/sdk/identity/Azure.Identity/README.md).
+
+## Examples
+
+Code samples for using the management library for .NET can be found in the following locations
+- [.NET Management Library Code Samples](https://aka.ms/azuresdk-net-mgmt-samples)
+
+## Troubleshooting
+
+-   File an issue via [GitHub Issues](https://github.com/Azure/azure-sdk-for-net/issues).
+-   Check [previous questions](https://stackoverflow.com/questions/tagged/azure+.net) or ask new ones on Stack Overflow using Azure and .NET tags.
+
+## Next steps
+
+For more information about Microsoft Azure SDK, see [this website](https://azure.github.io/azure-sdk/).
+
+## Contributing
+
+For details on contributing to this repository, see the [contributing
+guide][cg].
+
+This project welcomes contributions and suggestions. Most contributions
+require you to agree to a Contributor License Agreement (CLA) declaring
+that you have the right to, and actually do, grant us the rights to use
+your contribution. For details, visit <https://cla.microsoft.com>.
+
+When you submit a pull request, a CLA-bot will automatically determine
+whether you need to provide a CLA and decorate the PR appropriately
+(for example, label, comment). Follow the instructions provided by the
+bot. You'll only need to do this action once across all repositories
+using our CLA.
+
+This project has adopted the [Microsoft Open Source Code of Conduct][coc]. For
+more information, see the [Code of Conduct FAQ][coc_faq] or contact
+<[email protected]> with any other questions or comments.
+
+<!-- LINKS -->
+[cg]: https://github.com/Azure/azure-sdk-for-net/blob/main/sdk/resourcemanager/Azure.ResourceManager/docs/CONTRIBUTING.md
+[coc]: https://opensource.microsoft.com/codeofconduct/
+[coc_faq]: https://opensource.microsoft.com/codeofconduct/faq/