Sometimes the Postgresql Brew service isn't shut down correctly, due to a hard boot or OS crash, and the process id file (postmaster.pid) doesn't get removed.

fix-postgresql-brew-service-fails-to-start.md

1. Remove the old postmaster.pid file:

trash /usr/local/var/postgres/postmaster.pid
# or rm /usr/local/var/postgres/postmaster.pid

2. Restart the postgresql service:

brew services restart postgresql

To use the trash command, install the Trash CLI by Sindre Sorhus.

I found the answer on Stack Overflow: Cannot connect to Postgres server running through brew services