OSX: migrating Postgres db from one Mac to another

Hello,
my Mac unfortunately crashed. I have a Time Machine backup.
Using the Migration Assistant on a new Mac allowed me to get all my
documents back, but unfortunately Postgres is not able to start.

So I was trying to manually set-up my Postgres db.

Here are the steps:

- install a fresh copy of Postgres (v11)
- replace the /Library/PostgreSQL/11/data folder with the one I dig out
from my dead Mac, where I assume my data is stored
- check/fix owner of folders (must be 'postgres', I assume)
- start pgAdmin
- enter the PW for postgres user
- click on "PostgreSQL 11" server to show databases

This is where I have problems. I am prompted with the same pop-up asking me
to enter the password for the user 'postgres'. I type it and I get the
message "could not connect to server: Connection refused Is the server
running on host "localhost" (::1) and accepting TCP/IP connections on port
5432? could not connect to server: Connection refused Is the server running
on host "localhost" (127.0.0.1) and accepting TCP/IP connections on port
5432?