Right, those videos are getting a bit old by this point, but keep in mind that they're using ArcMap and an older workflow for a different purpose than what it sounds like you're doing from this post.
Here are a couple of distinctions that I think you'll find helpful:
1) There is a difference between calculating a walking Service Area around transit stops and a transit+walking Service Area for some facility.
A walking Service Area around a transit stop shows you the area within a short walk time or distance of the transit stop. To calculate this, you just need a road network. The network should not include the transit lines because you are not calculating travel by transit. You are simply calculating travel by walking. In this case the transit stops are the origins/destinations in the analysis, not part of the network. You can use the ArcGIS Online Services to calculate this.
A transit+walking Service Area answers the question "how far can I travel by transit and walking within a certain time limit?" It uses the transit lines as part of the network. The transit stops in this case are not the origins/destinations of the analysis but are instead part of the network. You cannot use the ArcGIS Online Services to calculate this. You will have to create your own network dataset that includes your GTFS data. The videos you're referring to are older and talk about the now-deprecated downloadable Add GTFS to a Network Dataset toolbox. You can now do this using core tools in ArcGIS Pro.
So, you need to be clear which of these things you're calculating, as that determines what kind of network you need to use.
2) "Generate Service Areas" refers to a particular tool, but this is not quite the same as solving a Service Area analysis generally. It's not always easy for me to tell which one you're referring to in a post, so that's why it's sometimes hard to answer your questions.
As explained in my earlier post, the Generate Service Areas tool in ArcGIS Pro is one of the Ready-to-Use tools that uses the ArcGIS Online Services to solve an analysis problem.
To make matters confusing, ArcMap has the same Generate Service Areas Ready-to-Use tool, but it also has a Generate Service Areas tool in the Services Tools toolset of the Network Analyst Tools toolbox, which allowed you to use your own network dataset.
However, both ArcMap and Pro allow you to solve a Service Area analysis using a multi-step workflow of
a) Make your Service Area layer
b) Add Facilities to the layer
c) Solve the layer
The video you're referring to does this procedure in ArcMap using a transit-enabled network dataset (the one made from OSM data for Cincinnati).
You can follow this tutorial to learn how to do this procedure in Pro. If you want to calculate a walking+transit Service Area in Pro, you will need to create a transit-enabled network dataset and then do this multi-step Service Area workflow. This tutorial can help you out with all of that.