Thank YunoGod it is finally fixed, I was pulling my hair out.
It was just a couple of easy things (I do not see any relationship between them) but, as they were happening at the same time, it looked very confusing.
I noticed the contents of my /etc/postfix/virtual-mailbox-domains file did not include my subdomain, only the domain. I just included the subdomain by enabling email for that subdomain on the domains section of the webadmin interface. That fixed the mail-loop-back-to-myself problem.
Then users started to receive incoming email. All but alice. But once email was working for everyone, alice’s problem was easy to solve.
root@subdomain:~# cd /var/mail
root@subdomain:/var/mail# ls -hal | grep alice
drwx--S--- 39 vmail mail 4.0K Aug 22 21:19 BOGUS.alice.f4A5
-rw-rw---- 1 alice mail 23K Aug 22 23:57 alice
root@subdomain:/var/mail#
root@subdomain:/var/mail# mkdir -p /root/alice-just-in-case-backup
root@subdomain:/var/mail# cp -a /var/mail/alice /var/mail/BOGUS.alice.f4A5 /root/alice-just-in-case-backup/
root@subdomain:/var/mail# rm alice
root@subsomain:/mai/mail# mv BOGUS.alice.f4A5 alice
root@subsomain:/mai/mail# systemctl restart dovecot
Thank you very much @jarod5001 and @rodinux for your help!