OK, your reply is very helpful and clarified a few things for me on how docker networking works. I see where you are leading me.
I had a little trouble with the command you provided for me. I get-
-bash jq .[].NetworkSettings.Networks: command not found
xargs: docker: terminated by signal 13
So I tried docker network ls, located the network name and ran docker network inspect mattermost_mattermost. I was at least able to see what the hostname and IP are for the DB. Though, that command does not show the extra info, like your command does I think it gets the job done for testing purpose. (unless there is something specific we need such as aliases) I can at least get the Name and IP address.
I did sustitute the IP address in MM_SQLSETTINGS_DATASOURCE to the IP address of the postgres container.
Presently my settings are:
MM_SQLSETTINGS_DATASOURCE=postgres://${POSTGRES_USER}:${POSTGRES_PASSWORD}@172.21.0.2:5432/${POSTGRES_DB}?sslmode=disable&connect_timeout=10
No change even after restarting MM container. 
I am guessing we need to find a way to make your command work so we can discover Aliases or something else?