A couple of things....
The diagram you've shown above is the 'Base Deployment' of ArcGIS Enterprise, that is, the minimum spec of an ArcGIS Enterprise you can deploy. Optional server roles can be appended:
https://enterprise.arcgis.com/en/get-started/latest/windows/additional-server-deployment.htm
One of those is a GIS Server. Which is like a hosting server but as this text:
https://enterprise.arcgis.com/en/get-started/latest/windows/additional-server-deployment.htm#ESRI_SE....
states, it should be considered to be different and 'should' be split out. It is the GIS Server that connets to any geodatabases.
In saying all of that, I would ask "Why do you want an Enterprise Geodatabase?" Don't get me wrong, they're great, but if you've got this far with file geodatabases then do you need to go 'bigger' and add more complexity?
You can use file geodatabases inside of ArcGIS Enterprise and they're 'fast'. Much simpler to deal with than Enterprise Geodatabases, and as wizgis has said, you have the option of the ArcGIS Data Store as well which coveres many use cases.
If you have a genuine need for the Enterprise Geodatabase, then do it. But don't go down that route because you 'assume' that you need an Enterprise Geodatabase to use ArcGIS Enterprise. Ultimately the Enterprise Geodatabase was around long before ArcGIS Enterprise was and is an option, but not a dependency.
Scott Tansley
https://www.linkedin.com/in/scotttansley/