IIRC cron writes stdout to the local mail spool (<user>@localhost). If the server is configured correctly, with an SMTP service for the domain, these emails are basically forwarded to <user>@<domain>

In practice, I have never seen a Linux server with an actual SMTP server configured correctly in 20 years, so the worst that usually happens is that cronjobs never actually leave the machine. You used to get a mail notification when you logged in if cron had written something, but that doesn’t happen anymore on recent distros.