Add core health monitoring infrastructure for vmcp backends

[yrobla]

Implement health checking and status tracking for virtual MCP server backends. This provides the foundation for monitoring backend availability and categorizing failure modes (unhealthy, degraded, unauthenticated).

Large PR Justification

This is an atomic commit, adding the core functionality for vmcp healthchecks. It includes comprehensive testing

Related-to: #3036

[github-actions]

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## Large PR Justification

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[codecov]

Codecov Report

❌ Patch coverage is 76.27628% with 79 lines in your changes missing coverage. Please review.
✅ Project coverage is 57.09%. Comparing base (aeab6bd) to head (8de8abb).
⚠️ Report is 3 commits behind head on main.

Files with missing lines	Patch %	Lines
pkg/vmcp/errors.go	0.00%	34 Missing ⚠️
pkg/vmcp/client/client.go	22.85%	20 Missing and 7 partials ⚠️
pkg/vmcp/health/checker.go	75.00%	6 Missing and 4 partials ⚠️
pkg/vmcp/health/monitor.go	94.82%	6 Missing ⚠️
pkg/vmcp/health/status.go	98.14%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3100      +/-   ##
==========================================
+ Coverage   56.89%   57.09%   +0.19%     
==========================================
  Files         337      341       +4     
  Lines       33617    33940     +323     
==========================================
+ Hits        19127    19378     +251     
- Misses      12899    12959      +60     
- Partials     1591     1603      +12     

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[Copilot]

Pull request overview

This PR implements core health monitoring infrastructure for virtual MCP (Model Context Protocol) server backends. It provides a foundation for tracking backend availability, detecting failure patterns, and categorizing different types of failures (unhealthy, degraded, unauthenticated).

Key changes:

• Health checker implementation using ListCapabilities as the health check mechanism with error categorization
• Status tracker with threshold-based failure detection and thread-safe state management
• Periodic health monitor with configurable intervals, automatic failure tracking, and graceful lifecycle management

Reviewed changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
pkg/vmcp/health/checker.go	Implements health checking using ListCapabilities with error categorization (auth, timeout, connection failures)
pkg/vmcp/health/checker_test.go	Comprehensive tests for health checker including error categorization, timeouts, and concurrent backend scenarios
pkg/vmcp/health/status.go	Status tracker for managing backend health states with threshold-based transitions and thread-safe operations
pkg/vmcp/health/status_test.go	Extensive tests for status tracking including concurrency, state transitions, and edge cases
pkg/vmcp/health/monitor.go	Periodic health monitor with background goroutines, configurable intervals, and lifecycle management
pkg/vmcp/health/monitor_test.go	Monitor tests covering start/stop lifecycle, periodic checks, context cancellation, and health summaries

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[github-actions]

✅ Large PR justification has been provided. The size review has been dismissed and this PR can now proceed with normal review.

Large PR justification has been provided. Thank you!

[Copilot]

Pull request overview

Copilot reviewed 10 out of 10 changed files in this pull request and generated 3 comments.

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[jhrozek]

Left a few observations from reviewing this PR. Nothing blocking, just some things to consider.