Add structured logging with log/slog

Replace fmt.Printf logging calls with slog.Info/slog.Error for structured
JSON output to stderr. Add internal/log package to initialize the default
slog handler from the config log level. Fix .gitignore to only ignore the
binary at the repo root, not the cmd/eng-pad-server directory.

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

internal/log/log.go

@@ -0,0 +1,23 @@
+package log
+
+import (
+	"log/slog"
+	"os"
+	"strings"
+)
+
+func Init(level string) {
+	var lvl slog.Level
+	switch strings.ToLower(level) {
+	case "debug":
+		lvl = slog.LevelDebug
+	case "warn":
+		lvl = slog.LevelWarn
+	case "error":
+		lvl = slog.LevelError
+	default:
+		lvl = slog.LevelInfo
+	}
+	handler := slog.NewJSONHandler(os.Stderr, &slog.HandlerOptions{Level: lvl})
+	slog.SetDefault(slog.New(handler))
+}