Why can't I set up a dovecot/exim4 mail server with a Permission denied error?

Question

Exim

Once I set up mail using the vestaPanel
, now I want to redo it - it doesn’t work for some reason, it
gives an error that there are not enough rights to write (I even set 777 to see if the error goes away, nothing changes)
dovecot logs

Apr 08 13:06:12 pop3-login: Info: Login: user=<alex>, method=PLAIN, rip=95.13.59.**, lip=46.101.186.***, mpid=29740, session=<TdpjcFNpmgBfDTsv>
Apr 08 13:06:12 pop3(alex): Error: user alex: Initialization failed: Initializing mail storage from mail_location setting failed: mkdir(/home/admin/mail//alex) failed: Permission denied (euid=1000(admin) egid=8(mail) missing +w perm: /home/admin/mail/, dir owned by 0:0 mode=0751)
Apr 08 13:06:12 pop3(alex): Error: Invalid user settings. Refer to server log for more information.

drwxrwxr-x   4 root root 4096 Apr  8 11:37 .
drwxr-xr-x 111 root root 4096 Apr  8 10:24 ..
drwxr-xr-x   2 root root 4096 Apr  9 12:09 conf.d
-rw-rw-r--   1 root root   90 Apr  7 10:42 dovecot.conf
drwx------   2 root root 4096 Apr  6 17:39 private
-rw-r--r--   1 root root  116 Mar  2 02:38 README.dpkg-dist

drwxr-xr-x 2 root root 4096 Apr  9 12:09 .
drwxrwxr-x 4 root root 4096 Apr  8 11:37 ..
-rw-r--r-- 1 root root  111 Sep 27  2013 10-auth.conf
-rw-r--r-- 1 root root   32 Sep 27  2013 10-logging.conf
-rw-r--r-- 1 root root  139 Apr  9 01:02 10-mail.conf
-rw-r--r-- 1 root root 3388 Apr  9 12:00 10-master.conf
-rw-r--r-- 1 root root  376 Apr  7 11:51 10-ssl.conf
-rw-r--r-- 1 root root  377 Apr  7 11:51 10-ssl.conf.vst.back
-rw-r--r-- 1 root root 2417 Sep 27  2013 20-imap.conf
-rw-r--r-- 1 root root 3729 Feb 11  2013 20-pop3.conf
-rw-r--r-- 1 root root  225 Apr  8 12:37 auth-passwdfile.conf.ext

Answer 1

Hello,
There is too much to assume... from crooked software configs to crooked owners in the system. Give configs, outputs of ls -al, for example, etc. Then you can give some advice.