feat(CF-2136): Add Sentry structured logging support

Enable enableLogs + beforeSendLog in Sentry.init, add log helpers where
applicable. Bump @sentry/node to ^10.39.0 for Sentry.logger API.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/index.ts

@@ -19,6 +19,11 @@ if (process.env.SENTRY_DSN) {
     dsn: process.env.SENTRY_DSN,
     environment: process.env.SENTRY_ENVIRONMENT || "production",
     tracesSampleRate: parseFloat(process.env.SENTRY_API_TRACE_RATE || "0.1"),
+    enableLogs: true,
+    beforeSendLog(log) {
+      if (log.level === "debug") return null;
+      return log;
+    },
   });
 }