Error while installing PostgreSQL 14.2 onto kUbuntu 20.04

i tried to install and get in run PostgreSQL 14.2 onto kUbuntu Version 20.04. using instructions from several pages and it ends always with the same error. i tried as described here:

1. https://www.postgresql.org/download/linux/ubuntu/
2. https://dev.to/monicag/install-postgresql-onto-ubuntu-multipass-vm-511p
3. https://itnixpro.com/install-postgresql-on-ubuntu/
4. https://techviewleo.com/how-to-install-postgresql-database-on-ubuntu/

example 2.

sudo sh -c 'echo "deb http://apt.postgresql.org/pub/repos/apt $(lsb_release -cs)-pgdg main" > /etc/apt/sources.list.d/pgdg.list'
sudo apt-get update
sudo apt-get -y install postgresql

sudo su - postgres
psql

before each installation try i cleaned the system like so:

sudo apt-get remove '^postgresql.*'  
sudo apt-get --purge remove postgresql postgresql-doc postgresql-common  
sudo rm -r /usr/lib/postgresql/  
sudo rm -r /var/lib/pgsql/data  
sudo rm -r /var/lib/postgresql/  
sudo rm -r /etc/postgresql  
sudo rm -r /var/run/postgresql/  
sudo rm -r /var/log/postgresql/  
reboot

the error always happens if i try this:

su - postgres  
psql

and sends this message:

# psql: error: connection to server on socket "/var/run/postgresql/.s.PGSQL.5432" failed: No such file or directory  
#        Is the server running locally and accepting connections on that socket?

After reading https://dba.stackexchange.com/questions/182189/how-do-i-access-postgres-when-i-get-an-error-about-var-run-postgresql-s-pgsql

i tried

unix_socket_directories = '/tmp/'

that not changed my error.

i heard that people switched to fedora because of some problems. i hope its possible to solve this without switching the Linux distribution.