Enhance server with context initialization and graceful shutdown

- Added context-aware server initialization in cmd/server/main.go
- Implemented graceful shutdown handling with SIGINT/SIGTERM signals
- Added 30-second shutdown timeout for active connections
- Updated Greet service to use context.Context as first parameter
- Enhanced Zerolog integration with Trace level logging
- Added context-aware logging in Greet function calls
- Fixed route structure to use /api/v1/greet/* prefix
- Updated all handlers and tests to use context
- Comprehensive AGENTS.md documentation with verified commands
- Added server context management architecture section
- Updated API endpoint documentation with working examples

Changes:
- cmd/server/main.go: Complete rewrite with context and graceful shutdown
- pkg/greet/greet.go: Added context parameter and trace logging
- pkg/greet/api_v1.go: Updated interface and handlers for context
- pkg/greet/greet_test.go: Updated tests to use context
- cmd/greet/main.go: Updated CLI to use context
- pkg/server/server.go: Trace level config and context logging
- AGENTS.md: Comprehensive documentation update
- go.mod/go.sum: Added Zerolog dependency

All tests passing, server working with graceful shutdown verified.

pkg/greet/api_v1.go

@@ -1,14 +1,16 @@
 package greet
 
 import (
+	"context"
 	"encoding/json"
 	"net/http"
 
 	"github.com/go-chi/chi/v5"
+	"github.com/rs/zerolog/log"
 )
 
 type Greeter interface {
-	Greet(name string) string
+	Greet(ctx context.Context, name string) string
 }
 
 type ApiV1Greet interface {
@@ -24,18 +26,20 @@ func NewApiV1GreetHandler(greeter Greeter) ApiV1Greet {
 }
 
 func (h *apiV1GreetHandler) RegisterRoutes(router chi.Router) {
+	log.Trace().Msg("Registering greet routes")
 	router.Get("/", h.handleGreetQuery)
 	router.Get("/{name}", h.handleGreetPath)
+	log.Trace().Msg("Greet routes registered")
 }
 
 func (h *apiV1GreetHandler) handleGreetQuery(w http.ResponseWriter, r *http.Request) {
 	name := r.URL.Query().Get("name")
-	h.writeJSONResponse(w, h.greeter.Greet(name))
+	h.writeJSONResponse(w, h.greeter.Greet(r.Context(), name))
 }
 
 func (h *apiV1GreetHandler) handleGreetPath(w http.ResponseWriter, r *http.Request) {
 	name := chi.URLParam(r, "name")
-	h.writeJSONResponse(w, h.greeter.Greet(name))
+	h.writeJSONResponse(w, h.greeter.Greet(r.Context(), name))
 }
 
 func (h *apiV1GreetHandler) writeJSONResponse(w http.ResponseWriter, message string) {