Publish NuGet gate tests to version-based drop path

[Nigusu-Allehu]

Bug

Fixes:
Related: https://github.com/NuGet/Client.Engineering/issues/3543

Description

Publishes gate test binaries and runsettings to a Tests/ drop pathvderived from the NuGet product version, enabling the runners to locate test drops by version.

• Add NuGet.Tests.Apex.Gate.runsettings for gate-filtered tests
• Publish test drop alongside existing product drop
• Tag test with [TestCategory("Gate")]

PR Checklist

• Meaningful title, helpful description and a linked NuGet/Home issue
• Added tests
• Link to an issue or pull request to update docs if this PR changes settings, environment variables, new feature, etc.