A great thing about ArcGIS Online is that there are several different ways to reach the same goal when it comes to making an application. Right now, I can find three methods to create an experience from a template:
1) Under the Content tab and My Content, select "Create App" and pick Experience Builder
2) Use the application launcher to select Experience Builder.
3) After creating a web map in Map Viewer, clicking the "Create App" on setting on the left side of the screen
However, you cannot view organizational templates or your own templates via option 3 and can only see ESRI choices. It would make more sense if these were in alignment and gave the user the same experience. It would also help organizations maintain consistency by granting access to organization templates through all methods of app creation.
Attached is an image of what the creation screen looks like for
