Is it possible to get an app for internal employees in the AppStore?
First, it is not possible for an organisation to get an internal app into Apple's App Store.

Most large organisations manage both corporate and BYOD devices using a Mobile Device Management (MDM) system.

My organisation uses AirWatch but others include JAMF, Microsoft InTune, SimpleMDM and Meraki.

An MDM can either deliver the app automatically or provide some form of self-service for internal apps.

All of the MDMs listed above have an associated cost. There are some open source MDMs available but at the moment they all seem more focussed on Mac management than iOS.