Hi Jesse
Have a read of this page - ArcGIS Pro license levels—ArcGIS Pro | Documentation
ArcGIS Pro users using Basic level cannot edit feature classes in a enterprise geodatabase. You need a Standard Level to begin to create and manage enterprise geodatabase artifacts, like relationship classes.
I am going to make a big assumption that you do not have Portal for ArcGIS and ArcGIS Server is not federated? If you do have both, then the ability to modify features via a feature service is managed by a staff members Portal user type (they must be signed into Portal as a Data Editor, Creator (user, data editor, publisher or administrator). An ArcGIS Pro Standard license is still required.
If not, then it would be determined by the Server users set up and capabilities configured in ArcGIS Server service and what credentials are provided when you create a new ArcGIS Server connection. This method is becoming less common in favour of using Portal for ArcGIS for authentication\authorization and privileges\roles across ArcGIS Enterprise. An ArcGIS Pro Standard license is still required. Editor permissions for feature services—ArcGIS Server | Documentation for ArcGIS Enterprise
ArcGIS Field Maps requires either Field Worker Named user type or Creator (with data editor, user or publisher role) to allow staff to be collect data in the field, both online and offline. To create ArcGIS Field Maps web maps, a member must be a Creator (publisher role). User types, roles, and privileges—ArcGIS Online Help | Documentation. If you use Field Maps or other Esri mobile applications for data collection, you do not require ArcGIS Pro for the same task.
Hope this information helps
Cheers Ed
