I actually figured this out; sharing here for anyone else who might need it!
There's a config file that needs to be modified in the container to allow the defined user to connect from anywhere (please make sure you handle security appropriately!):
docker exec 564 <CONTAINER> -c 'echo -e "\nhost all inedodb 0.0.0.0/0 md5" >> /var/lib/inedodb/data/pg_hba.conf'
Since this is inside the container, it will be overwritten by docker compose down -- so if there is a more ideal configuration, feel free to update the thread. If you're setting up from scratch like I did, the steps are:
docker compose up -dto create the containers- The
docker execcommand in the Postgres docs to init the DB and create the connection string - Editing
docker-compose.ymlwith the connection string docker compose down <PROGET_CONTAINER> && docker compose up -dto remake the app container