Update documentation with server package details

Add server package description, component table, and usage example to
README. Document server architecture, middleware chain, and test
conventions in CLAUDE.md.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

CLAUDE.md

@@ -13,6 +13,8 @@ go vet ./...                            # static analysis
 ## Architecture
 
 - **Module**: `git.codelab.vc/pkg/httpx`, Go 1.24, zero external dependencies
+
+### Client
 - **Core pattern**: middleware is `func(http.RoundTripper) http.RoundTripper`
 - **Chain assembly order** (client.go): Logging → User MW → Retry → CB → Balancer → Transport
   - Retry wraps CB+Balancer so each attempt can hit a different endpoint
@@ -21,10 +23,20 @@ go vet ./...                            # static analysis
 - **balancer.Transport** returns `(Middleware, *Closer)` — Closer must be tracked for health checker shutdown
 - **Client.Close()** stops the health checker goroutine
 
+### Server (`server/`)
+- **Core pattern**: middleware is `func(http.Handler) http.Handler`
+- **Server** wraps `http.Server` with `net.Listener`, graceful shutdown via signal handling, lifecycle hooks
+- **Router** wraps `http.ServeMux` — supports groups with prefix + middleware inheritance, `Mount` for sub-handlers
+- **Middleware chain** via `Chain(A, B, C)` — A outermost, C innermost (same as client side)
+- **statusWriter** wraps `http.ResponseWriter` to capture status; implements `Unwrap()` for `http.ResponseController`
+- **Defaults()** preset: RequestID → Recovery → Logging + production timeouts
+- **HealthHandler** exposes `GET /healthz` (liveness) and `GET /readyz` (readiness with pluggable checkers)
+
 ## Conventions
 
-- Functional options for all configuration
-- Test helpers: `mockTransport(fn)` wrapping `middleware.RoundTripperFunc`
+- Functional options for all configuration (client and server)
+- Test helpers: `mockTransport(fn)` wrapping `middleware.RoundTripperFunc` (client), `httptest.NewRecorder`/`httptest.NewRequest` (server)
+- Server tests use `waitForAddr(t, srv)` helper to poll until server is ready
 - No external test frameworks — stdlib only
 - Thread safety required (`sync.Mutex`/`atomic`)
 - `internal/clock` for deterministic time testing