GrapheneOs ships with a a few basic apps, and it has no stores. To have access to stores you have to install them.
There are 4 major places to install apps from; Google Play store, Aurora Store, Fdroid store, and github/gitlab.
To install Google play you use an app called "Apps" in GrapheneOS. Then you can install and use google play store. It seems this has already been installed for you since you see the icon. You will need a google account to use this.
Aurora gets all its apps from google play store and gives them to you without needing a google account. You can install Aurora store from here: https://gitlab.com/AuroraOSS/AuroraStore
To get fdroid apps you should install an fdroid "client" which accesses the fdroid database and installs apps for you. Droid-ify is a good fdroid client app that can do that for you. you can get it here: https://github.com/Iamlooker/Droid-ify. Go to "releases" section for the apk file.
Another app called "Obtanium" can be used to update apk files you have installed directly from github/gitlab. Get it here: https://github.com/ImranR98/Obtainium