feat(logging): integrate slog logging with env control and request/sync tracing

- Configure structured slog logger in cmd/server/main.go via LOG_LEVEL and DEBUG env vars
- Add HTTP API request logging middleware in internal/api/ with status and duration_ms
- Add WebSocket join/leave, event reception, and debounced SQLite flush tracing in docroom
- Document LOG_LEVEL and DEBUG settings in .env.example, compose.yaml, and docker-compose.yml

internal/ws/hub.go

@@ -3,7 +3,7 @@ package ws
 import (
 	"encoding/json"
 	"fmt"
-	"log"
+	"log/slog"
 	"net/http"
 	"strings"
 	"sync"
@@ -627,7 +627,7 @@ func (c *Client) SendEvent(event string, payload interface{}) {
 func (h *Hub) ServeWS(w http.ResponseWriter, r *http.Request, roomID, userID string) {
 	conn, err := upgrader.Upgrade(w, r, nil)
 	if err != nil {
-		log.Printf("[ws] upgrade error: %v", err)
+		slog.Error("WebSocket upgrade error", "room_id", roomID, "user_id", userID, "error", err)
 		return
 	}