mrivera,
Welcome. Running pgAdmin4 doesn't require you to be running, nor start running a local postgreSQL server. There may be some confusion in that pgAdmin *itself* is a server (just not a postgreSQL server). Actually pgAdmin4 is just the back end, it relies on a browser to provide a user interface (UI). It can be set up in two modes; 'server' mode (which is rather confusing I'll admit) and 'desktop' mode. The major difference between the two is that in 'desktop' mode it doesn't require you to login, whereas 'server' mode is designed to be run on a separate machine and accessed over the network requiring users to provide login credentials to pgAdmin4 itself, in addition to any credentials needed to log into a particular instance of postgreSQL.
So, if you are running on a constrained laptop, I would be careful to go into your taskbar (assuming you are running Windows) and use the pgAdmin4 icon to stop the server when you are finished using it. It will restart the next time you try to run pgAdmin4. Admittedly it would be helpful if there was a setting that automatically stopped the pgAdmin4 server from continuing to run after the last browser window was closed and it is configured in 'desktop' mode. Perhaps someday.
I hope that helps,
rik.