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/webserver/server.go

@@ -6,6 +6,7 @@ import (
 	"fmt"
 	"html/template"
 	"io/fs"
+	"log/slog"
 	"net/http"
 	"time"
 
@@ -85,10 +86,10 @@ func Start(cfg Config) (*http.Server, error) {
 			Certificates: []tls.Certificate{tlsCert},
 			MinVersion:   tls.VersionTLS13,
 		}
-		fmt.Printf("Web UI listening on %s (TLS)\n", cfg.Addr)
+		slog.Info("web UI started", "addr", cfg.Addr, "tls", true)
 		go func() { _ = srv.ListenAndServeTLS("", "") }()
 	} else {
-		fmt.Printf("Web UI listening on %s\n", cfg.Addr)
+		slog.Info("web UI started", "addr", cfg.Addr, "tls", false)
 		go func() { _ = srv.ListenAndServe() }()
 	}