Restrict App Store Apps

Not that I'm aware of. You can restrict which apps can be used on a device with a Restrictions payload (iOS and tvOS/Applications). So if there are any that you really don't want on there you can say "Do Not Allow Some Apps," and then add those to your list. Not the most elegant, but it gets the job done for us...

I know you said you don't want to block the App Store completely, but would that still be the case if the approved App Store apps were available for your users in Self Service?

You can make your "work-related" App Store apps available in Self Service using VPP, and advise your users to grab their apps from there as opposed to the App Store. The good thing about Self Service is that it's like your own custom company App Store, so if you have that set up you can just prevent your users from launching the native App Store.

If this is on Mac OS you can also configure a "Restricted Software" record to block the App Store and give an advisory message to direct the users towards Self Service. Something like this:

Microsoft Apps wont install when App store is restricted.. I tried and it failed. Then, when I allowed access to App store, they installed fine.
So, maybe not all Apps can be made available this way.

In my environment we have the App Store restricted completely and the only way to get App Store apps is through SelfService. When someone wants an app added to SelfService they request it and it goes through a vetting process and is either made available or not. Shifting from letting the users use the App Store directly to SelfService is probably the most direct way to get the control you want. Baring that you would need to look at black listing everything that you dont want using restrictions or external tools which would be a lot of work, white listing is also an option but can also be a lot of work. JAMF does not really offer either of these functions in a usable fashion you are needing from the way it sounds..

I was able to restrict the App Store completely under a couple of departments. However, using the same bundle ID in the new department isn't blocking the App Store from populating on the iPads. Does anyone know what the correct bundle ID is for the App Store? I was using com.apple.AppStore - but this doesn't seem to work anymore.

Any updates on this case. I have encountered the same issue that apps won't get installed via Self Service if app store is blocked.