How to deny access to Postgres when connected from host/non-local

Hello,

I try to deny access to all databases on my server if the user “postgres" tries to connect from a non-local host. Here is what I did in pg_hba.conf:

# TYPE DATABASE USER ADDRESS METHOD

# "local" is for Unix domain socket connections only
local all all md5
# IPv4 local connections:
host all all 127.0.0.1/32 md5
# IPv6 local connections:
host all all ::1/128 md5
# Allow replication connections from localhost, by a user with the
# replication privilege.
local replication all md5
host replication all 127.0.0.1/32 md5
host replication all ::1/128 md5
host all all 0.0.0.0/0 md5
local all postgres trust
host all postgres 0.0.0.0/0 reject

But it continues to allow for Postgres to connect from anywhere through PGAdmin but also as a direct connection to port 5432. I also relaunched the server. This is version 12.

What else do I have to do?

Thanks for any help.

Cheers,
Alex