Improve connection tests

[mbg]

A few minor improvements to the private registry connection checks:

• Use GET instead of HEAD requests, for better compatibility. Some registries don't like HEAD requests. We still call res.destroy() immediately after inspecting the status code, so never read the response body. So using GET over HEAD should have a minimal impact on performance.
• For NuGet feeds, we now test the service index instead of the base URL. The service index should always be present and is more reliable than making a request to the base URL.
• Some logging improvements.

Risk assessment

For internal use only. Please select the risk level of this change:

• Low risk: Changes are fully under feature flags, or have been fully tested and validated in pre-production environments and are highly observable, or are documentation or test only.

Which use cases does this change impact?

Workflow types:

• Managed - Impacts users with dynamic workflows (Default Setup, Code Quality, ...).

Products:

• Code Scanning - The changes impact analyses when analysis-kinds: code-scanning.
• Code Quality - The changes impact analyses when analysis-kinds: code-quality.
• Other first-party - The changes impact other first-party analyses.

Environments:

• Dotcom - Impacts CodeQL workflows on github.com and/or GitHub Enterprise Cloud with Data Residency.
• GHES - Impacts CodeQL workflows on GitHub Enterprise Server.

How did/will you validate this change?

• Unit tests - I am depending on unit test coverage (i.e. tests in .test.ts files).
• End-to-end tests - I am depending on PR checks (i.e. tests in pr-checks).

If something goes wrong after this change is released, what are the mitigation and rollback strategies?

• Rollback - Change can only be disabled by rolling back the release or releasing a new version with a fix.

How will you know if something goes wrong after this change is released?

• Telemetry - I rely on existing telemetry or have made changes to the telemetry.
  • Dashboards - I will watch relevant dashboards for issues after the release. Consider whether this requires this change to be released at a particular time rather than as part of a regular release.
  • Alerts - New or existing monitors will trip if something goes wrong with this change.

Are there any special considerations for merging or releasing this change?

• No special considerations - This change can be merged at any time.

Merge / deployment checklist

• Confirm this change is backwards compatible with existing workflows.
• Consider adding a changelog entry for this change.
• Confirm the readme and docs have been updated if necessary.

[Copilot]

Pull request overview

Improves the private registry reachability checks used by the start-proxy action, aiming to make the connectivity tests more compatible across different registry implementations and provide clearer logging.

Changes:

• Switch the reachability probe request from HEAD to GET while still not reading the body (res.destroy() immediately).
• Add registry-type-specific test URL handling (NuGet: test service index).
• Add a doc link disclaimer and group logging around connection tests.

Show a summary per file

File	Description
src/start-proxy/reachability.ts	Updates request method to GET, adds NuGet-specific test URL logic, and improves logging (group + disclaimer).
src/start-proxy-action.ts	Clarifies comment that registry checks are best-effort.
src/doc-url.ts	Adds a documentation URL for private registry diagnostic logs.
lib/start-proxy-action.js	Generated JS output corresponding to TS changes (not reviewed).

Copilot's findings

• Files reviewed: 3/4 changed files
• Comments generated: 2