To get enterprise feature, including authentication feature (compatible with enterprise authentication), you should consider RStudio Products. Either Shiny Server or RStudio Connect. They are made for this, making it the easier solution, but yes at a cost. It is also the easier solution if you need integration between the login and your app.
On the on premise product side, there is also ShinyProxy, an OSS product for deploying dockerized shiny app. it has an authentication feature. However, you need to know docker for using this.
Another solution, as you are on premise, is that you can (with help of your IT teams) create a setup where you server serving the shiny apps is behing some proxy that needs to be pass through with authentication. You may already have a solution at work for that. Otherwise, in this configure, the shinyapps server can't be reach without passing through another login service.
If you can go to the cloud, shinyapps.io pro feature allows you to get login for your app.
At last, on the R package side, there are some work from appsilon that can help
I hope this will help you.