Accepted Solutions
I added the server to the project and opened Catalog View, right clicked on the server and clicked on properties to change the user type. I read in another thread that you had to be an admin to publish and publishing is not an option when you right click. I am an admin.
Please follow the steps in order.
Use "Add Server" for adding an existing connection file. Else use "New ArcGIS Server" for creating a new connection file.
For a standalone server (not federated), I am able to change the Connection Type from Server's Properties (after the connection is created).
With a Publisher Connection, I can publish Map Service, Image Service and Geocode Service.
With an Administrator Connection, I can additionally publish Geoprocessing Service as well.
Configurations for ArcGIS Server
If you have access to ArcGIS Server Manager, check the following page
Login to ArcGIS Server Manager > Security > Settings
A stand-alone Server should look similar to this (if using built-in users)
A federated Server should look similar to this (this one is also a hosting server)
*NOTE: If your ArcGIS Server site is federated, you can still use the same process to publish from ArcMap, but you can't publish directly from ArcGIS Pro.
I will share further steps, if you can confirm if your ArcGIS Server site is federated with ArcGIS Enterprise.