I don't think that the pgAdmin user and the database user are necessarily the same thing (though I could be wrong) [see: https://www.pgadmin.org/docs/pgadmin4/5.4/user_management.html ]. The pg_hba.conf file defines what users/machines/methods are allowed to connect to a postgresql server. So for the first line in your example:
host all all my.dbserver.ip.addr/32 trust
this would mean; host == connections made over TCP/IP, the first all == which databases, the second all == which users, the my.dbserver.ip.addr/32 == means only allow connections originating from that exact ip address, and trust == allow connections without a password or any other form of authentication [see: https://www.postgresql.org/docs/13/auth-pg-hba-conf.html ]. I am guessing that you have gotten the pgAdmin users confused with the postgresql database users.
I would imagine that the pgAdmin server would need an entry in the pg_hba.conf file for whatever machine pgAdmin is running on and I would be amazed if it was using trust (or no authentication) to connect with. I use pgAdmin exclusively in desktop mode, so hopefully someone else who's more familiar with server mode will chime in.
After getting pgadmin4 installed and configured, I've found out that the user credentials I specified during the setup don't work very well. I've added the user to the postgres db using the adduser command. I updated the pg_hba.conf file with an entry just for the user but I get this error when trying to connect for the 1st time:
FATAL: no pg_hba.conf entry for host " my.dbserver.ip.addr", user "p@p.com", database "postgres", SSL off
So to make it work, I'd just like to set the username/password to the postgres user. Where can I do that? I don't see a .py or .conf file other than pg_hba.conf where the user is defined.