Could not connect to server when PostgreSQL at new storage location

Question

I am trying to change the data directory of my PostgreSQL db on my Raspberry pi 4.

The steps I performed are:

1. Installing PostgreSQL:

   sudo apt install postgresql

2. Stopping service:

   sudo service postgresql stop

3. Move database files (which I tryed in two ways)

   sudo mv /var/lib/postgresql/11/main /mnt/storage/postgres

   OR

   sudo rsync -av /var/lib/postgresql/11/main /mnt/storage/postgres

4. Adapting postgresql.conf

   data_directory = '/mnt/storage/postgres'

   listen_addresses = '*'

5. Starting service:

   sudo service postgresql start

With the command "psql" I receive the following output:

psql: could not connect to server: No such file or directory
        Is the server running locally and accepting
        connections on Unix domain socket "/var/run/postgresql/.s.PGSQL.5432"?

---

Additional Information:

$ service postgresql status
● postgresql.service - PostgreSQL RDBMS
   Loaded: loaded (/lib/systemd/system/postgresql.service; enabled; vendor preset: enabled)
   Active: active (exited) since Fri 2022-02-04 17:12:29 CET; 31s ago
  Process: 21169 ExecStart=/bin/true (code=exited, status=0/SUCCESS)
 Main PID: 21169 (code=exited, status=0/SUCCESS)

Feb 04 17:12:29 MyPi systemd[1]: Starting PostgreSQL RDBMS...
Feb 04 17:12:29 MyPi systemd[1]: Started PostgreSQL RDBMS.

$cat /etc/os-release
PRETTY_NAME="Raspbian GNU/Linux 10 (buster)"
NAME="Raspbian GNU/Linux"
VERSION_ID="10"
VERSION="10 (buster)"
VERSION_CODENAME=buster
ID=raspbian
ID_LIKE=debian
HOME_URL="http://www.raspbian.org/"
SUPPORT_URL="http://www.raspbian.org/RaspbianForums"
BUG_REPORT_URL="http://www.raspbian.org/RaspbianBugs"

$ psql -V
psql (PostgreSQL) 11.14 (Raspbian 11.14-0+deb10u1)

$ findmnt
...
/mnt/storage                        /dev/sda1      fuseblk    rw,relatime,user_id=0,group_id=0,default_permissions,allow_other,blksize=4096
...

Update:

$ pg_lsclusters
Ver Cluster Port Status Owner Data directory                           Log file
11  main    5432 down   root  /mnt/storage/postgres/postgresql/11/main /var/log/postgresql/postgresql-11-main.log

The location I want to use for the database is an external drive. I played also around with permission and ownership of the mounted external drive. One issue I am experiencing here is that the permissions always return to their initial state after I changed them.

$ cat /etc/fstab
...
PARTUUID=96082d9d-0e40-4ac9-821b-78d65ae2c3f0 /mnt/storage ntfs-3g auto,users,permissions 0 0
...