"We are adding your app" message only showing, but not getting deploy when trying to add app into SharePoint on-premises environment. App installation service timer is not running as per the schedule When checking the services related to the app management. Also, the job is not executing even when using the run now option. I don't see any logs related to this issue in Event Viewer or ULS logs. I have followed many ways by restarting the timer services, cache clear of time service and account permission check. Did anyone face such issue? If so please share your thoughts.
Try to restart SharePoint Timer service and SharePoint Administration service.
After that, do an IISRESET.
A similar thread for your reference:
installing SharePoint 2013 application does not finish