Handling of local mail by Postfix

I have three servers (web, social, mail) on which a root cronjob is executed nightly. For two of the servers (web, social), the cron notification is delivered through the local Postfix MTA to the third server (mail, the actual mail server for my domain) where it ends up in a virtual mailbox provided by Dovecot:

Delivered-To: mailer@example.org
Received: from mail.example.org
        by mail.example.org with LMTP
        id wDFyCv3VI2ivHSYAkvmB9w
        (envelope-from )
        for ; Wed, 14 May 2025 01:30:05 +0200
Received: by web.example.org (Postfix)
        id B93541C7A31; Wed, 14 May 2025 01:30:02 +0200 (CEST)
Delivered-To: root@web.example.org
Received: by web.example.org (Postfix, from userid 0)
        id B25781C7A32; Wed, 14 May 2025 01:30:02 +0200 (CEST)
From: Cron Daemon 
To: root@web.example.org
Subject: Cron  /root/scripts/config_backup.py

The translation of the local root account (root@web.example.org) to mailer@example.org is supposedly based on /etc/aliases, which contains

root: mailer@example.org
default: mailer@example.org

and is referenced in /etc/postfix/main.cf (alias_maps = hash:/etc/aliases), although there is no /etc/aliases.db as with other Postfix lookup tables. There is also /etc/mail.rc, which contains

alias root root

but this is probably not used by Postfix. The third server (mail) has the exact same configuration with respect to aliases, but the cron notification is handled locally and never reaches the Dovecot mailbox (mailer@example.org) on the server:

From root@mail.example.org Mon May 12 01:30:02 2025
Return-Path: 
X-Original-To: root
Delivered-To: root@mail.example.org
Received: by mail.example.org (Postfix, from userid 0)
        id 4A07D8180F; Mon, 12 May 2025 01:30:02 +0000 (UTC)
From: root@mail.example.org (Cron Daemon)
To: root@mail.example.org
Subject: Cron  /root/scripts/config_backup.py

I am confused – why does the mail server handle the messages differently?