Is App Shop's constant connection safe?

[Rindourei]

Considering it seems to be norm it is likely safe, but I'll still ask.
While I do need to log in to install some apps, when opening App Shop, it recognizes my username. It also checks for app updates.
If such connection is open, is there any possibility my Apple Password could be stolen while surfing or logged into some forum? I think there was a way to completely log out so it doesn't even recognize me when opening App Shop. Should I do that for security?

 

[Partron22]

If there's no connection, there's no place to mount a man in the middle attack.
That said, I've not heard of any such attacks on MacOS/Store connection.
iOS App/store connections, sure. Don't know about the store app itself on iOS to the App store.
If you don't want to find out the connection is insecure the hard way, turn it off when you're not actively using it.