Remove dead code and redundant ping timeout in health check

[gkatz2]

Bug description

PR #4108 made health check parameters configurable but left behind two cleanup items identified during review:

1. Two dead zero-value guards in transparent_proxy.go that can never trigger, since the constructor and functional options guarantee positive values for healthCheckInterval and healthCheckPingTimeout.

2. A hardcoded context.WithTimeout(ctx, 5*time.Second) in healthcheck.go:checkMCPStatus that redundantly wraps the ping call. The MCPPinger already enforces its own timeout via http.Client.Timeout (set to the configured value through TOOLHIVE_HEALTH_CHECK_PING_TIMEOUT). The redundant context timeout silently caps the configured ping timeout at 5s — if a user sets TOOLHIVE_HEALTH_CHECK_PING_TIMEOUT=10s for a slow backend, the context cancels first and the configured value is ineffective.

Steps to reproduce

1. Set TOOLHIVE_HEALTH_CHECK_PING_TIMEOUT=10s
2. The transparent proxy's MCPPinger is correctly created with a 10s HTTP client timeout
3. But checkMCPStatus wraps the ping in context.WithTimeout(ctx, 5*time.Second), which fires first

Expected behavior

The configured ping timeout should be the effective timeout for health check pings.

Actual behavior

The hardcoded 5s context timeout in checkMCPStatus overrides any configured value above 5s.

Additional context

• jhrozek identified both issues during PR Make transparent proxy health check parameters configurable #4108 review (inline comment, review comment) and agreed a follow-up PR is fine (comment).
• The fix removes the redundant context timeout rather than plumbing the configured value through HealthChecker. Both existing MCPPinger implementations handle timeouts internally: the transparent proxy pinger uses http.Client.Timeout, and the httpsse pinger is non-blocking (fire-and-forget channel send). The HealthChecker doesn't need to duplicate timeout enforcement that the pinger already owns.
• The equivalent dead guard for retryDelay was already removed in PR Make transparent proxy health check parameters configurable #4108 commit a41f8a87.