[HealthChecks] Register health check services & checks

[jviau]

Issue describing the changes in this PR

Part of #11010, #11168

Pull request checklist

IMPORTANT: Currently, changes must be backported to the in-proc branch to be included in Core Tools and non-Flex deployments.

• Backporting to the in-proc branch is not required
  • Otherwise: Link to backporting PR
• My changes do not require documentation changes
  • Otherwise: Documentation issue linked to PR
• My changes should not be added to the release notes for the next release
  • Otherwise: I've added my notes to release_notes.md
• My changes do not need to be backported to a previous version
  • Otherwise: Backport tracked by issue/PR #issue_or_pr
• My changes do not require diagnostic events changes
  • Otherwise: I have added/updated all related diagnostic events and their documentation (Documentation issue linked to PR)
• I have added all required tests (Unit tests, E2E tests)

Additional information

Registers health check services and 2 health checks for the web and script host lifecycle. Release notes are not yet updated as these services are still not yet consumed, and thus no runtime impact (yet)

[Copilot]

Pull Request Overview

This PR registers health check services and implements two health checks for monitoring the web host and script host lifecycles in Azure Functions. It replaces FluentAssertions with AwesomeAssertions across test files and adds comprehensive health check infrastructure.

• Adds health check registration to the web host service collection
• Implements WebHostHealthCheck and ScriptHostHealthCheck with lifecycle monitoring
• Creates standardized health check names and tags for Azure Functions
• Replaces FluentAssertions with AwesomeAssertions in test files

Reviewed Changes

Copilot reviewed 12 out of 12 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
WebJobs.Script.Tests.csproj	Replaces FluentAssertions package with AwesomeAssertions
AppServiceHeaderFixupMiddlewareTests.cs	Updates using statement for new assertion library
OpenTelemetryConfigurationExtensionsTests.cs	Updates using statement for new assertion library
WebHostHealthCheckTests.cs	Updates using statement for new assertion library
ScriptHostHealthCheckTests.cs	Updates using statement for new assertion library
HealthCheckExtensionsTests.cs	New test file for health check extension methods
WebHostHealthCheck.cs	Adds XML documentation for the web host health check
ScriptHostHealthCheck.cs	Adds XML documentation for the script host health check
HealthCheckTags.cs	New file defining standardized health check tags
HealthCheckNames.cs	New file defining standardized health check names
HealthCheckExtensions.cs	New file with extension methods for registering health checks
WebHostServiceCollectionExtensions.cs	Registers health check services in the web host

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[Copilot]

The callback in this test setup captures a registration parameter but only assigns to a local variable that isn't used. This appears to be leftover debugging code that should be removed for clarity.

Suggested change

	});
	builder.Setup(b => b.Add(It.IsAny<HealthCheckRegistration>())).Returns(builder.Object);