.NET: Improve resilience of verify-samples by building separately and improving evaluation instructions

[westey-m]

Motivation and Context

• Moving to a newer model resulted in poorer structured output compliance
• Running sample builds in parallel causes failures that are not sample related.

Description

• Default to building samples separately
• Improve instructions and structured output model to improve output compliance

Contribution Checklist

• The code builds clean without any errors or warnings
• The PR follows the Contribution Guidelines
• All unit tests pass, and I have added new tests where possible
• Is this a breaking change? If yes, add "[BREAKING]" prefix to the title of the PR.

[Copilot]

Pull request overview

This PR updates the .NET verify-samples tool to reduce flakiness from parallel sample builds by defaulting to running samples with dotnet run --no-build (assuming a prior build step), and refines the AI-verifier prompt/schema to improve structured output compliance.

Changes:

• Add a --build option to control whether sample projects are built during execution (default: do not build).
• Update sample execution to pass --no-build by default, plus documentation/workflow updates to build the solution first.
• Improve AI verification instructions and structured response schema (including stderr in the prompt).

Reviewed changes

Copilot reviewed 7 out of 7 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
dotnet/eng/verify-samples/VerifyOptions.cs	Adds CLI flag parsing for --build and exposes BuildSamples option.
dotnet/eng/verify-samples/VerificationOrchestrator.cs	Threads buildSamples through orchestration into sample runs.
dotnet/eng/verify-samples/SampleVerifier.cs	Enhances AI verification prompt/schema and includes stderr in the verification prompt.
dotnet/eng/verify-samples/SampleRunner.cs	Implements --no-build default behavior and adds a build parameter.
dotnet/eng/verify-samples/Program.cs	Wires BuildSamples into the orchestrator and updates usage comment.
dotnet/.github/skills/verify-samples-tool/SKILL.md	Documents the new default pre-build requirement and the --build escape hatch.
.github/workflows/dotnet-verify-samples.yml	Builds the solution before running verify-samples in CI.