If you open one of the Data Model PDFs listed at the bottom, there are links there
Which one did you open? Most of them I looked at don't have the Design Templates links, or at least the links to Visio templates.
The overall problem with the Data Models is that they are just that, data models. The OP wants templates/shapes for system or IT models.
I used the attached stencil that I created for the images in this help article. Maybe they'll serve as a start.
Thank you Jonathan Quinn
I found an icon set for contemporary slideshows (2019) on a Google Drive Folder. Looks like Esri but provenance is not clear.
I also found a repository of SVG icons.
I prefer the old icons Esri used, but those are not turning up.
Matthew, the Icons8 site is interesting, I hadn't seen those GIS icons before. In fact, I am slightly surprised a generic graphic design site has a "GIS" section.
Regarding the Google Drive folder contents, they are from Esri although Esri didn't post them. Another GeoNet member in https://community.esri.com/message/689802-arcgis-icon-library-for-architecture mentions they came from an Esri distributor.