Update internal publishing to use fine-grained publishing targets for .NET 10 channels

[Copilot]

Summary

This PR implements fine-grained asset category-based publishing for .NET 10 internal channels, mirroring the behavior already used by public .NET 10 channels. This ensures that infrastructure and tooling packages are published to their dedicated internal feeds rather than the general .NET 10 internal feeds.

Problem

Previously, all .NET 10 internal channel packages were published to either dotnet10-internal (shipping) or dotnet10-internal-transport (non-shipping) feeds, regardless of the asset category. This differed from the public channels, which route packages based on their category:

• Infrastructure packages → dotnet-eng
• Tooling packages → dotnet-tools
• Library packages → dotnet-libraries feeds
• Core/regular packages → version-specific feeds

Solution

Updated DotNet10InternalFeeds to use the same fine-grained targeting approach:

Asset Category	Feed (Shipping)	Feed (Non-Shipping)
InfrastructurePackage	dotnet-eng-internal	dotnet-eng-internal
ToolingPackage	dotnet-tools-internal	dotnet-tools-internal
LibraryPackage	dotnet-libraries-internal	dotnet-libraries-internal-transport
CorePackage	dotnet10-internal	dotnet10-internal-transport
Package	dotnet10-internal	dotnet10-internal-transport

Changes

1. Added new feed constant:

   • FeedDotNetEngInternal for infrastructure packages
   • Uses existing FeedDotNetToolsInternal for tooling packages (both shipping and non-shipping)

2. Updated DotNet10InternalFeeds array to route by asset category (14 feed specifications total, up from 4)

Impact

This change affects all .NET 10 internal channels:

• .NET 10 Internal (5177)
• .NET 10 Private (8710)
• .NET 10.0.1xx SDK Internal (5178, 8858)
• .NET 10.0.2xx SDK Internal (8857, 8861)
• .NET 10 RC 2 Internal (6500, 6579)

Testing

• All existing tests pass (180 passed, 1 skipped)
• Build completes successfully

Fixes: Context from https://github.com/dotnet/release/issues/1617

• Fixes Update internal publishing to use fine-grained publishing targets based on asset category for dotnet 10 internal channels #16242

Original prompt

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This section details on the original issue you should resolve

<issue_title>Update internal publishing to use fine-grained publishing targets based on asset category for dotnet 10 internal channels</issue_title>
<issue_description>Update internal publishing so that internal eng and tools assets are pushed to dotnet-eng-internal and dotnet-tools-internal-transport/dotnet-tools, respectively. This should mirror the behavior of public promotion and be implemented for all .NET 10 channels. See PublishingConstants.cs

Context: https://github.com/dotnet/release/issues/1617

• This issue is blocking
• This issue is causing unreasonable pain

Comments on the Issue (you are @copilot in this section)

• Fixes Update internal publishing to use fine-grained publishing targets based on asset category for dotnet 10 internal channels #16242

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