It's smart of you to still use the App Store logo though. ;) I'll give you that.
To me the icon indicating it's app store is this: https://developer.apple.com/app-store/marketing/guidelines/#...
But now you actually got me wondering if I should change it.
Personally I thought that it would either open the app store, or that is was something related to Apple pay (although that one needs "[logo] Pay").
It felt a bit misleading.
Edit: In fact, thinking about it some more, it's very clearly much closer to the App Store logo than anything else. It's literally the white silhouette design from the logo (as opposed to the colored non-sillhouete version from generic app icons), placed on a blue button that's similar to the app store logo's blue background.
The folder on my mac uses that icon for Applications.