[HealthChecks] Add health check middleware

[jviau]

Issue describing the changes in this PR

Part of #11010, #11171

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

Adds supporting files for the eventual addition of a health check endpoint. The added files do two primary things:

1. HealthCheckWaitMiddleware.cs -- this file enables HTTP long polling of health probes by adding a ?wait={timeInSeconds} query string to the health check calls.
2. HealthCheckResponseWriter -- this files writes the HTTP responses for health checks. It has 2 modes, a minimal or an expanded response.
   • The expanded response is provided by AspNetCore.Diagnostics.HealthChecks. This ensures it is compatible with other components from that ecosystem of health check packages.
   • Minimal/expanded response is controlled by ?expand={true/false}. Default is false if not included.
   • Note this intentionally does not set status code. That will be done by the AspNetCore health check middleware (which will be added later)

This PR also removes ApiErrorModel (it is unused) and introduces ErrorResponse, which is modeled after the ARM recommended error structure.

[liliankasem]

lgtm, minor comments. deps json looks good, I don't see any major version bumps

[Copilot]

Pull Request Overview

This PR adds health check middleware infrastructure to support health check endpoints with two main features: long polling capabilities and configurable response formats. It removes the unused ApiErrorModel class and introduces a new ARM-compliant ErrorResponse model.

• Adds HealthCheckWaitMiddleware to enable HTTP long polling via ?wait={seconds} query parameter
• Adds HealthCheckResponseWriter to handle both minimal and expanded health check responses via ?expand={true/false}
• Replaces deprecated ApiErrorModel with ARM-compliant ErrorResponse model

Reviewed Changes

Copilot reviewed 20 out of 20 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
HealthCheckWaitMiddleware.cs	Implements long polling for health checks with wait parameter support
HealthCheckResponseWriter.cs	Handles response formatting with minimal/expanded modes
ErrorResponse.cs	New ARM-compliant error model replacing deprecated ApiErrorModel
ScriptHostManagerExtensions.cs	Renames method to DelayUntilHostReadyAsync for consistency
Test files	Comprehensive unit tests for new middleware and response writer

[kshyju]

nit: Not sure we should mention "used across the functions host". I prefer something along the line of "Shared Json serializer with the following settings: 1) Trailing commas allowed, 2) camel casing ...."

[kshyju]

Remove unnecessary usings.