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/server/server.go

@@ -4,6 +4,7 @@ import (
 	"crypto/tls"
 	"database/sql"
 	"fmt"
+	"log/slog"
 	"net/http"
 	"time"
 
@@ -42,7 +43,7 @@ func Start(cfg Config) (*http.Server, error) {
 		IdleTimeout:  120 * time.Second,
 	}
 
-	fmt.Printf("REST API listening on %s\n", cfg.Addr)
+	slog.Info("REST API started", "addr", cfg.Addr)
 	go func() { _ = srv.ListenAndServeTLS("", "") }()
 
 	return srv, nil