For those who are curious, I was able to connect successfully with the changes to my code below. I changed "localserver" to "127.0.0.1". It then spat out some role error, so I went into the database and played around the roles for the db and now it seems to be good. I'll post any new discoveries here since I haven't seen many people post about this stuff on the board, and I wish there were more here about it.
OpenSQLConnection[JDBC["PostgreSQL", "127.0.0.1:5432/world_db"],
"Username" -> "postgres", "Password" -> "$Prompt"]
The $Prompt is great because you can just type any username and password right in there!
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