Looking at documentation, since I'm going to be running PGadmin III on a different computer, it seems like I'll need to allow the PostgreSQL server to accept outside connections.

Entorno de desarrollo local con PostgreSQL 17.5 y pgAdmin 4 en Docker para Windows, con volúmenes mapeados a rutas locales.

To install PostgreSQL on Windows 11, run PostgreSQL installer to install Postgres and then connect it to PostgreSQL using PgAdmin.