Update image and build run-name on internal only

[MiYanni]

Summary

This PR updates the agent images used by both the PR build and the official build (internal). I've consolidated where the image is declared into a variable for each pipeline-type respectively, AgentImagePublic and AgentImageInternal.

The reason to update these images was the current VS2022 image was causing build failures for this PR that updates the version of Arcade:

##[error].dotnet\sdk\10.0.100\Sdks\Microsoft.NET.Sdk\targets\Microsoft.NET.Sdk.DefaultItems.targets(145,5): error NETSDK1233: (NETCORE_ENGINEERING_TELEMETRY=Build) Targeting .NET 10.0 or higher in Visual Studio 2022 17.14 is not supported.

So, I've selected the current available image for VS2026 respectively (public and internal), windows.vs2026preview.scout.amd64.open and windows.vs2026preview.scout.amd64.

Additionally, I noticed the run name updating logic in the build was applying to the PR build. This was not intentional. So, I've added a condition to only allow that target to run internally.

Official Test Run

• https://dnceng.visualstudio.com/internal/_build/results?buildId=2854983