You have to pay for the Network Analyst extension for Enterprise, and to build the data you have to have Network Analyst for ArcGIS Pro too (It's two separate licenses).
The Esri way for handling real time data is called "GeoEvent Server"
https://enterprise.arcgis.com/en/geoevent/latest/get-started/what-is-arcgis-geoevent-server.htm
I have never needed it but I've always assumed it would cost way more than I could justify. It is separate from ArcGIS Server (not just an extension) and they suggest you run it on a separate machine. Of course it depends on your own usage.
Where would you be getting the traffic data?
I just tried the traffic map in ArcGIS.com https://clatsopcounty.maps.arcgis.com/apps/mapviewer/index.html?webmap=bbdcd78953e5439985004023c8eda... and found it to be meaningless for my area. Could be fine for you?
I'd probably look at something from a third party like maybe WAZE? I'd look for "freemium" services because at my usage levels just about everything I need is free. I love being able to start free and try out services without investment. WAZE is "free" which means you pay them somehow probably by giving them all your data. Also they are owned by Google now but maybe you are okay with that.
