TIFU by letting pacman upgrade the postgresql a major version (13->14). Then the postgresql service failed to start.. Anyways here is the fix.

also a nice thing in the AUR: the postgresql-old-upgrade package. It provides the binary for the older version of psql under/opt/postgresql{VERSION}

Before doing anything stop the postgresql service.

mv /var/lib/postgres/data /var/lib/postgres/olddata
mkdir /var/lib/postgres/data /var/lib/postgres/tmp
chown postgres:postgres /var/lib/postgres/data /var/lib/postgres/tmp

# SWITCH TO postgres user: sudo -iu postgres

cd /var/lib/postgres/tmp

initdb -D /var/lib/postgres/data --PARAMETERS_USED_TO_INIT_DB

pg_upgrade -b /opt/pgsql-PG_VERSION/bin -B /usr/bin -d /var/lib/postgres/olddata -D /var/lib/postgres/data

Then start postgresql.service again

Thank you, archwiki.