Add examples/ with runnable usage demos for all major features

Six examples covering the full API surface:
- basic-client: retry, timeout, logging, response size limit
- form-request: form-encoded POST for OAuth/webhooks
- load-balancing: weighted endpoints, circuit breaker, health checks
- server-basic: routing, groups, JSON helpers, health, custom 404
- server-protected: CORS, rate limiting, body limits, timeouts
- request-id-propagation: cross-service request ID forwarding

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

examples/request-id-propagation/main.go

@@ -0,0 +1,54 @@
+// Demonstrates request ID propagation between server and client.
+// The server assigns a request ID to incoming requests, and the client
+// middleware forwards it to downstream services via X-Request-Id header.
+package main
+
+import (
+	"fmt"
+	"log"
+	"log/slog"
+	"net/http"
+
+	"git.codelab.vc/pkg/httpx"
+	"git.codelab.vc/pkg/httpx/middleware"
+	"git.codelab.vc/pkg/httpx/server"
+)
+
+func main() {
+	logger := slog.Default()
+
+	// Client that propagates request IDs from context.
+	client := httpx.New(
+		httpx.WithBaseURL("http://localhost:9090"),
+		httpx.WithMiddleware(
+			middleware.RequestID(), // Picks up ID from context, sets X-Request-Id.
+		),
+	)
+	defer client.Close()
+
+	r := server.NewRouter()
+
+	r.HandleFunc("GET /proxy", func(w http.ResponseWriter, r *http.Request) {
+		// The request ID is in r.Context() thanks to server.RequestID().
+		id := server.RequestIDFromContext(r.Context())
+		logger.Info("handling request", "request_id", id)
+
+		// Client automatically forwards the request ID to downstream.
+		resp, err := client.Get(r.Context(), "/downstream")
+		if err != nil {
+			server.WriteError(w, http.StatusBadGateway, fmt.Sprintf("downstream error: %v", err))
+			return
+		}
+		defer resp.Close()
+
+		body, _ := resp.String()
+		server.WriteJSON(w, http.StatusOK, map[string]string{
+			"request_id":          id,
+			"downstream_response": body,
+		})
+	})
+
+	// Server with RequestID middleware that assigns IDs to incoming requests.
+	srv := server.New(r, server.Defaults(logger)...)
+	log.Fatal(srv.ListenAndServe())
+}