Sorry, it's just not possible for us to determine what's going on based on the screenshots. It's likely still a problem with the geometry of the features or the restriction attributes of the entrances and exits (if something is restricted, it won't be counted as an exit).
Have you tried this scenario in ArcGIS Pro? The entire directions engine was updated in ArcGIS Pro and may behave slightly differently. I still think this is probably a geometry or network configuration problem rather than a bug in ArcMap's code, but it's still worth a try to see if Pro's directions engine behaves differently with this data. Here is a tutorial showing you how to do it: https://pro.arcgis.com/en/pro-app/latest/help/analysis/networks/route-tutorial.htm
If that doesn't fix it, you should probably contact Esri Support or Support from your Esri distributor if you're outside the US. They can look at your data and help you debug the problem in detail. If they can't resolve the issue, they will request help from our team (Network Analyst development team). Note that ArcMap is now in "mature support", which means you can still get technical support, but the expectation is that you are actively migrating your workflows to ArcGIS Pro because ArcMap is headed toward retirement as a product.
Good luck!